## Properties

Many properties of a natural number n can be seen or directly computed from the prime factorization of n.

• The multiplicity of a prime factor p of n is the largest exponent m for which pm divides n. The tables show the multiplicity for each prime factor. If no exponent is written then the multiplicity is 1 (since p = p1). The multiplicity of a prime which does not divide n may be called 0 or may be considered undefined.
• Ω(n), the big Omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities).
• A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, E, 11, 15, 17, 1E, 25, 27, 31. There are many special types of prime numbers.
• A composite number has Ω(n) > 1. The first: 4, 6, 8, 9, X, 10, 12, 13, 14, 16, 18, 19. All numbers above 1 are either prime or composite. 1 is neither.
• A semiprime has Ω(n) = 2 (so it is composite). The first: 4, 6, 9, X, 12, 13, 19, 1X, 21, 22, 29, 2X.
• A k-almost prime (for a natural number k) has Ω(n) = k (so it is composite if k > 1).
• An even number has the prime factor 2. The first: 2, 4, 6, 8, X, 10, 12, 14, 16, 18, 1X, 20.
• An odd number does not have the prime factor 2. The first: 1, 3, 5, 7, 9, E, 11, 13, 15, 17, 19, 1E. All integers are either even or odd.
• A square has even multiplicity for all prime factors (it is of the form a2 for some a). The first: 1, 4, 9, 14, 21, 30, 41, 54, 69, 84, X1, 100.
• A cube has all multiplicities divisible by 3 (it is of the form a3 for some a). The first: 1, 8, 23, 54, X5, 160, 247, 368, 509, 6E4, 92E, 1000.
• A perfect power has a common divisor m > 1 for all multiplicities (it is of the form am for some a > 1 and m > 1). The first: 4, 8, 9, 14, 21, 23, 28, 30, 41, 54, 69, 84. 1 is sometimes included.
• A powerful number (also called squareful) has multiplicity above 1 for all prime factors. The first: 1, 4, 8, 9, 14, 21, 23, 28, 30, 41, 54, 60.
• A prime power has only one prime factor. The first: 2, 3, 4, 5, 7, 8, 9, E, 11, 14, 15, 17. 1 is sometimes included.
• An Achilles number is powerful but not a perfect power. The first: 60, 90, 148, 200, 288, 300, 358, 460, 483, 568, 600, 688.
• A square-free integer has no prime factor with multiplicity above 1. The first: 1, 2, 3, 5, 6, 7, X, E, 11, 12, 13, 15. A number where some but not all prime factors have multiplicity above 1 is neither square-free nor squareful.
• The Liouville function λ(n) is 1 if Ω(n) is even, and is -1 if Ω(n) is odd.
• The Möbius function μ(n) is 0 if n is not square-free. Otherwise μ(n) is 1 if Ω(n) is even, and is −1 if Ω(n) is odd.
• A sphenic number has Ω(n) = 3 and is square-free (so it is the product of 3 distinct primes). The first: 26, 36, 56, 5X, 66, 86, 89, 92, 96, XX, E6, 10X.
• a0(n) is the sum of primes dividing n, counted with multiplicity. It is an additive function.
• A Ruth-Aaron pair is two consecutive numbers (x, x+1) with a0(x) = a0(x+1). The first (by x value): 5, 8, 13, 65, X5, 4E6, 670, 92X, X68, 10E2, 1537, 1X68, another definition is the same prime only count once, if so, the first (by x value): 5, 20, 41, 65, 88, 109, 269, 350, 4E6, E82, 1277, 13E7.
• A primorial x# is the product of all primes from 2 to x. The first: 2, 6, 26, 156, 1406, 15466, 207526, 32E92E6, 62868806, 130682E526, 32X53376556, 9EX23222X9E6. 1# = 1 is sometimes included.
• A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 20, X0, 500, 2E00, 1E400, 156000, 1270000, 11450000, 114500000. 0! = 1 is sometimes included.
• A k-smooth number (for a natural number k) has largest prime factor ≤ k (so it is also j-smooth for any j > k).
• m is smoother than n if the largest prime factor of m is below the largest of n.
• A regular number (number whose reciprocal is terminating dozenal) has no prime factor above 3 (so it is 3-smooth). The first: 1, 2, 3, 4, 6, 8, 9, 10, 14, 16, 20, 23.
• A k-powersmooth number has all pmk where p is a prime factor with multiplicity m.
• A frugal number has more digits than the number of digits in its prime factorization (when written like below tables with multiplicities above 1 as exponents). The first in dozenal: 183, 194, 247, 368, 441, 509, 714, 92E, 1054, 10X1, 1103, 1228.
• An equidigital number has the same number of digits as its prime factorization. The first in dozenal: 1, 2, 3, 5, 7, E, 11, 12, 13, 14, 15, 17.
• An extravagant number has fewer digits than its prime factorization. The first in dozenal: 4, 6, 8, 9, X, 10, 16, 18, 20, 22, 24, 26.
• An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital.
• gcd(m, n) (greatest common divisor of m and n) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n).
• m and n are coprime (also called relatively prime) if gcd(m, n) = 1 (meaning they have no common prime factor).
• lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n).
• gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.
• m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n.

The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown in table of divisors.

## Table

number prime factorization number prime factorization number prime factorization
1 unit 401 prime 801 prime
2 prime 402 2 × 152 802 2 × 401
3 prime 403 3 × 141 803 3 × 5 × 7 × E
4 22 404 22 × 5 × 25 804 22 × 152
5 prime 405 7 × 6E 805 11 × 75
6 2 × 3 406 2 × 3 × 81 806 2 × 3 × 141
7 prime 407 E × 45 807 17 × 51
8 23 408 23 × 61 808 23 × 5 × 25
9 32 409 32 × 5 × 11 809 33 × 37
X 2 × 5 40X 2 × 205 80X 2 × 7 × 6E
E prime 40E prime 80E prime
10 22 × 3 410 22 × 3 × 72 810 22 × 3 × 81
11 prime 411 17 × 27 811 5 × 175
12 2 × 7 412 2 × 5 × 4E 812 2 × E × 45
13 3 × 5 413 3 × 145 813 3 × 285
14 24 414 24 × 31 814 24 × 61
15 prime 415 prime 815 7 × 11E
16 2 × 32 416 2 × 33 × E 816 2 × 32 × 5 × 11
17 prime 417 5 × 7 × 15 817 prime
18 22 × 5 418 22 × 105 818 22 × 205
19 3 × 7 419 3 × 147 819 3 × 15 × 1E
1X 2 × E 41X 2 × 11 × 1E 81X 2 × 40E
1E prime 41E prime 81E 52 × 3E
20 23 × 3 420 23 × 3 × 52 820 23 × 3 × 72
21 52 421 prime 821 E × 8E
22 2 × 11 422 2 × 7 × 37 822 2 × 17 × 27
23 33 423 32 × 57 823 32 × XE
24 22 × 7 424 22 × 107 824 22 × 5 × 4E
25 prime 425 5 × E2 825 prime
26 2 × 3 × 5 426 2 × 3 × 85 826 2 × 3 × 145
27 prime 427 prime 827 7 × 112
28 25 428 25 × 17 828 25 × 31
29 3 × E 429 3 × 7 × 25 829 3 × 5 × 67
2X 2 × 15 42X 2 × 5 × 51 82X 2 × 415
2E 5 × 7 42E 11 × 3E 82E prime
30 22 × 32 430 22 × 32 × 15 830 22 × 33 × E
31 prime 431 prime 831 25 × 35
32 2 × 17 432 2 × 217 832 2 × 5 × 7 × 15
33 3 × 11 433 3 × 5 × 35 833 3 × 291
34 23 × 5 434 23 × 7 × E 834 23 × 105
35 prime 435 prime 835 prime
36 2 × 3 × 7 436 2 × 3 × 87 836 2 × 3 × 147
37 prime 437 prime 837 5 × 17E
38 22 × E 438 22 × 5 × 27 838 22 × 11 × 1E
39 32 × 5 439 33 × 1E 839 32 × 7 × 17
3X 2 × 1E 43X 2 × 21E 83X 2 × 41E
3E prime 43E 7 × 75 83E E × 91
40 24 × 3 440 24 × 3 × 11 840 24 × 3 × 52
41 72 441 54 841 prime
42 2 × 52 442 2 × 221 842 2 × 421
43 3 × 15 443 3 × E × 17 843 3 × 295
44 22 × 11 444 22 × 111 844 22 × 7 × 37
45 prime 445 15 × 31 845 5 × 181
46 2 × 33 446 2 × 32 × 5 × 7 846 2 × 32 × 57
47 5 × E 447 prime 847 15 × 5E
48 23 × 7 448 23 × 67 848 23 × 107
49 3 × 17 449 3 × 157 849 3 × 11 × 27
4X 2 × 25 44X 2 × 225 84X 2 × 5 × E2
4E prime 44E 5 × X7 84E 7 × 125
50 22 × 3 × 5 450 22 × 3 × 45 850 22 × 3 × 85
51 prime 451 72 × 11 851 prime
52 2 × 27 452 2 × E × 25 852 2 × 427
53 32 × 7 453 32 × 5E 853 35 × 5
54 26 454 27 × 5 854 26 × 17
55 5 × 11 455 prime 855 prime
56 2 × 3 × E 456 2 × 3 × 8E 856 2 × 3 × 7 × 25
57 prime 457 prime 857 1E × 45
58 22 × 15 458 22 × 7 × 1E 858 22 × 5 × 51
59 3 × 1E 459 3 × 5 × 37 859 3 × E × 31
5X 2 × 5 × 7 45X 2 × 15 × 17 85X 2 × 11 × 3E
5E prime 45E prime 85E prime
60 23 × 32 460 23 × 34 860 23 × 32 × 15
61 prime 461 E × 4E 861 52 × 72
62 2 × 31 462 2 × 52 × 11 862 2 × 431
63 3 × 52 463 3 × 7 × 27 863 3 × 2X1
64 22 × 17 464 22 × 117 864 22 × 217
65 7 × E 465 prime 865 prime
66 2 × 3 × 11 466 2 × 3 × 91 866 2 × 3 × 5 × 35
67 prime 467 5 × XE 867 prime
68 24 × 5 468 24 × 35 868 24 × 7 × E
69 34 469 32 × 61 869 32 × E5
6X 2 × 35 46X 2 × 7 × 3E 86X 2 × 435
6E prime 46E prime 86E 5 × 11 × 17
70 22 × 3 × 7 470 22 × 3 × 5 × E 870 22 × 3 × 87
71 5 × 15 471 prime 871 prime
72 2 × 37 472 2 × 237 872 2 × 437
73 3 × 25 473 3 × 11 × 15 873 3 × 7 × 4E
74 23 × E 474 23 × 6E 874 23 × 5 × 27
75 prime 475 5 × 7 × 17 875 15 × 61
76 2 × 32 × 5 476 2 × 32 × 31 876 2 × 33 × 1E
77 7 × 11 477 1E × 25 877 E × 95
78 22 × 1E 478 22 × 11E 878 22 × 21E
79 3 × 27 479 3 × 167 879 3 × 5 × 6E
7X 2 × 3E 47X 2 × 5 × 57 87X 2 × 7 × 75
7E 5 × 17 47E E × 51 87E 25 × 37
80 25 × 3 480 25 × 3 × 7 880 25 × 3 × 11
81 prime 481 prime 881 prime
82 2 × 72 482 2 × 241 882 2 × 54
83 32 × E 483 33 × 52 883 32 × E7
84 22 × 52 484 22 × 112 884 22 × 221
85 prime 485 prime 885 7 × 12E
86 2 × 3 × 15 486 2 × 3 × 95 886 2 × 3 × E × 17
87 prime 487 7 × 81 887 5 × 18E
88 23 × 11 488 23 × 5 × 15 888 23 × 111
89 3 × 5 × 7 489 3 × 16E 889 3 × 2XE
8X 2 × 45 48X 2 × E × 27 88X 2 × 15 × 31
8E prime 48E prime 88E prime
90 22 × 33 490 22 × 32 × 17 890 22 × 32 × 5 × 7
91 prime 491 5 × E5 891 11 × 81
92 2 × 5 × E 492 2 × 73 892 2 × 447
93 3 × 31 493 3 × 171 893 3 × 2E1
94 24 × 7 494 24 × 37 894 24 × 67
95 prime 495 11 × 45 895 5 × E × 1E
96 2 × 3 × 17 496 2 × 3 × 5 × 1E 896 2 × 3 × 157
97 5 × 1E 497 prime 897 7 × 131
98 22 × 25 498 22 × 125 898 22 × 225
99 32 × 11 499 32 × 7 × E 899 33 × 3E
9X 2 × 4E 49X 2 × 24E 89X 2 × 5 × X7
9E 7 × 15 49E 5 × E7 89E 27 × 35
X0 23 × 3 × 5 4X0 23 × 3 × 25 8X0 23 × 3 × 45
X1 E2 4X1 15 × 35 8X1 17 × 57
X2 2 × 51 4X2 2 × 251 8X2 2 × 72 × 11
X3 3 × 35 4X3 3 × 175 8X3 3 × 52 × 15
X4 22 × 27 4X4 22 × 52 × 7 8X4 22 × E × 25
X5 53 4X5 prime 8X5 prime
X6 2 × 32 × 7 4X6 2 × 33 × 11 8X6 2 × 32 × 5E
X7 prime 4X7 17 × 31 8X7 prime
X8 27 4X8 26 × E 8X8 28 × 5
X9 3 × 37 4X9 3 × 5 × 3E 8X9 3 × 7 × 51
XX 2 × 5 × 11 4XX 2 × 255 8XX 2 × 455
XE prime 4XE 7 × 85 8XE prime
E0 22 × 3 × E 4E0 22 × 3 × 4E 8E0 22 × 3 × 8E
E1 7 × 17 4E1 prime 8E1 5 × 195
E2 2 × 57 4E2 2 × 5 × 5E 8E2 2 × 457
E3 33 × 5 4E3 32 × 67 8E3 32 × E × 11
E4 23 × 15 4E4 23 × 75 8E4 23 × 7 × 1E
E5 prime 4E5 1E × 27 8E5 prime
E6 2 × 3 × 1E 4E6 2 × 3 × 7 × 15 8E6 2 × 3 × 5 × 37
E7 prime 4E7 5 × E × 11 8E7 prime
E8 22 × 5 × 7 4E8 22 × 12E 8E8 22 × 15 × 17
E9 3 × 3E 4E9 3 × 17E 8E9 3 × 2EE
EX 2 × 5E 4EX 2 × 25E 8EX 2 × 45E
EE E × 11 4EE prime 8EE 5 × 7 × 31
100 24 × 32 500 24 × 32 × 5 900 24 × 34
101 5 × 25 501 7 × 87 901 prime
102 2 × 61 502 2 × 172 902 2 × E × 4E
103 3 × 72 503 3 × 181 903 3 × 301
104 22 × 31 504 22 × 131 904 22 × 52 × 11
105 prime 505 52 × 25 905 prime
106 2 × 3 × 52 506 2 × 3 × E2 906 2 × 3 × 7 × 27
107 prime 507 prime 907 prime
108 23 × 17 508 23 × 7 × 11 908 23 × 117
109 32 × 15 509 36 909 32 × 5 × 25
10X 2 × 7 × E 50X 2 × 5 × 61 90X 2 × 465
10E 5 × 27 50E 15 × 37 90E prime
110 22 × 3 × 11 510 22 × 3 × 51 910 22 × 3 × 91
111 prime 511 prime 911 7 × E × 15
112 2 × 67 512 2 × 267 912 2 × 5 × XE
113 3 × 45 513 3 × 5 × 72 913 3 × 17 × 1E
114 25 × 5 514 25 × 1E 914 25 × 35
115 7 × 1E 515 E × 57 915 11 × 85
116 2 × 34 516 2 × 32 × 35 916 2 × 32 × 61
117 prime 517 prime 917 5 × 19E
118 22 × 35 518 22 × 5 × 31 918 22 × 7 × 3E
119 3 × 5 × E 519 3 × 11 × 17 919 3 × 307
11X 2 × 6E 51X 2 × 7 × 45 91X 2 × 46E
11E prime 51E prime 91E prime
120 23 × 3 × 7 520 23 × 3 × 27 920 23 × 3 × 5 × E
121 112 521 5 × 105 921 prime
122 2 × 5 × 15 522 2 × 271 922 2 × 471
123 32 × 17 523 32 × 6E 923 33 × 72
124 22 × 37 524 22 × E × 15 924 22 × 237
125 prime 525 7 × 8E 925 52 × 45
126 2 × 3 × 25 526 2 × 3 × 53 926 2 × 3 × 11 × 15
127 52 × 7 527 prime 927 prime
128 24 × E 528 24 × 3E 928 24 × 6E
129 3 × 4E 529 3 × 18E 929 3 × 30E
12X 2 × 75 52X 2 × 11 × 25 92X 2 × 5 × 7 × 17
12E prime 52E 5 × 107 92E E3
130 22 × 32 × 5 530 22 × 33 × 7 930 22 × 32 × 31
131 prime 531 prime 931 27 × 37
132 2 × 7 × 11 532 2 × 277 932 2 × 1E × 25
133 3 × 51 533 3 × E × 1E 933 3 × 5 × 75
134 23 × 1E 534 23 × 5 × 17 934 23 × 11E
135 5 × 31 535 prime 935 7 × 13E
136 2 × 3 × 27 536 2 × 3 × X7 936 2 × 3 × 167
137 E × 15 537 7 × 91 937 11 × 87
138 22 × 3E 538 22 × 13E 938 22 × 5 × 57
139 33 × 7 539 32 × 5 × 15 939 32 × 105
13X 2 × 5 × 17 53X 2 × 27E 93X 2 × E × 51
13E prime 53E 11 × 4E 93E 15 × 67
140 26 × 3 540 28 × 3 940 26 × 3 × 7
141 prime 541 prime 941 5 × 1X5
142 2 × 81 542 2 × 5 × 7 × E 942 2 × 481
143 3 × 5 × 11 543 3 × 195 943 3 × 315
144 22 × 72 544 22 × 141 944 22 × 241
145 prime 545 prime 945 17 × 5E
146 2 × 32 × E 546 2 × 32 × 37 946 2 × 33 × 52
147 prime 547 52 × 27 947 7 × 141
148 23 × 52 548 23 × 81 948 23 × 112
149 3 × 57 549 3 × 7 × 31 949 3 × E × 35
14X 2 × 85 54X 2 × 285 94X 2 × 485
14E 7 × 25 54E 17 × 35 94E 5 × 1X7
150 22 × 3 × 15 550 22 × 3 × 5 × 11 950 22 × 3 × 95
151 5 × 35 551 E × 5E 951 1E × 4E
152 2 × 87 552 2 × 15 × 1E 952 2 × 7 × 81
153 32 × 1E 553 33 × 25 953 32 × 107
154 24 × 11 554 24 × 72 954 24 × 5 × 15
155 E × 17 555 5 × 111 955 prime
156 2 × 3 × 5 × 7 556 2 × 3 × XE 956 2 × 3 × 16E
157 prime 557 prime 957 25 × 3E
158 22 × 45 558 22 × 145 958 22 × E × 27
159 3 × 5E 559 3 × 19E 959 3 × 5 × 7 × 11
15X 2 × 8E 55X 2 × 5 × 67 95X 2 × 48E
15E 5 × 37 55E 7 × 95 95E prime
160 23 × 33 560 23 × 32 × E 960 23 × 32 × 17
161 7 × 27 561 11 × 51 961 312
162 2 × 91 562 2 × 291 962 2 × 5 × E5
163 3 × 61 563 3 × 5 × 45 963 3 × 321
164 22 × 5 × E 564 22 × 147 964 22 × 73
165 11 × 15 565 prime 965 prime
166 2 × 3 × 31 566 2 × 3 × 7 × 17 966 2 × 3 × 171
167 prime 567 15 × 3E 967 53 × E
168 25 × 7 568 25 × 52 968 25 × 37
169 32 × 52 569 32 × 75 969 34 × 15
16X 2 × 95 56X 2 × 295 96X 2 × 11 × 45
16E prime 56E E × 61 96E 7 × 145
170 22 × 3 × 17 570 22 × 3 × 57 970 22 × 3 × 5 × 1E
171 prime 571 5 × 7 × 1E 971 prime
172 2 × 5 × 1E 572 2 × 11 × 27 972 2 × 497
173 3 × 7 × E 573 3 × 1X5 973 3 × 325
174 23 × 25 574 23 × 85 974 23 × 125
175 prime 575 prime 975 5 × 1E1
176 2 × 32 × 11 576 2 × 34 × 5 976 2 × 32 × 7 × E
177 5 × 3E 577 prime 977 17 × 61
178 22 × 4E 578 22 × 7 × 25 978 22 × 24E
179 3 × 67 579 3 × 1X7 979 3 × 327
17X 2 × 7 × 15 57X 2 × E × 31 97X 2 × 5 × E7
17E prime 57E 5 × 117 97E 11 × 8E
180 24 × 3 × 5 580 24 × 3 × 15 980 24 × 3 × 25
181 prime 581 17 × 37 981 7 × 147
182 2 × E2 582 2 × 2X1 982 2 × 15 × 35
183 35 583 32 × 7 × 11 983 32 × 5 × 27
184 22 × 51 584 22 × 5 × 35 984 22 × 251
185 5 × 72 585 prime 985 E × X7
186 2 × 3 × 35 586 2 × 3 × E5 986 2 × 3 × 175
187 11 × 17 587 prime 987 prime
188 23 × 27 588 23 × 87 988 23 × 52 × 7
189 3 × 6E 589 3 × 52 × E 989 3 × 32E
18X 2 × 53 58X 2 × 7 × 4E 98X 2 × 4X5
18E prime 58E prime 98E 1E × 51
190 22 × 32 × 7 590 22 × 32 × 1E 990 22 × 33 × 11
191 E × 1E 591 prime 991 5 × 1E5
192 2 × X7 592 2 × 5 × 6E 992 2 × 17 × 31
193 3 × 5 × 15 593 3 × 1E1 993 3 × 7 × 57
194 28 594 26 × 11 994 27 × E
195 prime 595 72 × 15 995 prime
196 2 × 3 × 37 596 2 × 3 × E7 996 2 × 3 × 5 × 3E
197 7 × 31 597 5 × 11E 997 15 × 6E
198 22 × 5 × 11 598 22 × E × 17 998 22 × 255
199 32 × 25 599 33 × 27 999 32 × 111
19X 2 × XE 59X 2 × 2XE 99X 2 × 7 × 85
19E prime 59E prime 99E 5 × 1E7
1X0 23 × 3 × E 5X0 23 × 3 × 5 × 7 9X0 23 × 3 × 4E
1X1 5 × 45 5X1 252 9X1 11 × 91
1X2 2 × 7 × 17 5X2 2 × 2E1 9X2 2 × 4E1
1X3 3 × 75 5X3 3 × 1E5 9X3 3 × E × 37
1X4 22 × 57 5X4 22 × 157 9X4 22 × 5 × 5E
1X5 prime 5X5 5 × 112 9X5 72 × 25
1X6 2 × 33 × 5 5X6 2 × 32 × 3E 9X6 2 × 32 × 67
1X7 prime 5X7 7 × E2 9X7 prime
1X8 24 × 15 5X8 24 × 45 9X8 24 × 75
1X9 3 × 7 × 11 5X9 3 × 1E7 9X9 3 × 52 × 17
1XX 2 × E5 5XX 2 × 52 × 15 9XX 2 × 1E × 27
1XE 52 × E 5XE 1E × 31 9XE prime
1E0 22 × 3 × 1E 5E0 22 × 3 × 5E 9E0 22 × 3 × 7 × 15
1E1 prime 5E1 prime 9E1 prime
1E2 2 × E7 5E2 2 × 7 × 51 9E2 2 × 5 × E × 11
1E3 32 × 27 5E3 32 × 5 × 17 9E3 33 × 45
1E4 23 × 5 × 7 5E4 23 × 8E 9E4 23 × 12E
1E5 prime 5E5 prime 9E5 prime
1E6 2 × 3 × 3E 5E6 2 × 3 × E × 11 9E6 2 × 3 × 17E
1E7 prime 5E7 prime 9E7 5 × 7 × 35
1E8 22 × 5E 5E8 22 × 5 × 37 9E8 22 × 25E
1E9 3 × 5 × 17 5E9 3 × 7 × 35 9E9 3 × 33E
1EX 2 × E × 11 5EX 2 × 2EE 9EX 2 × 4EE
1EE 7 × 35 5EE prime 9EE prime
200 25 × 32 600 25 × 33 X00 25 × 32 × 5
201 152 601 5 × 125 X01 E × XE
202 2 × 5 × 25 602 2 × 301 X02 2 × 7 × 87
203 3 × 81 603 3 × 152 X03 3 × 11 × 31
204 22 × 61 604 22 × 7 × 27 X04 22 × 172
205 prime 605 E × 67 X05 5 × 152
206 2 × 3 × 72 606 2 × 3 × 5 × 25 X06 2 × 3 × 181
207 5 × 4E 607 11 × 57 X07 prime
208 23 × 31 608 23 × 91 X08 23 × 131
209 33 × E 609 32 × 81 X09 32 × 7 × 1E
20X 2 × 105 60X 2 × 17 × 1E X0X 2 × 52 × 25
20E 11 × 1E 60E 53 × 7 X0E prime
210 22 × 3 × 52 610 22 × 3 × 61 X10 22 × 3 × E2
211 7 × 37 611 prime X11 prime
212 2 × 107 612 2 × 307 X12 2 × 507
213 3 × 85 613 3 × 205 X13 3 × 5 × 81
214 24 × 17 614 24 × 5 × E X14 24 × 7 × 11
215 5 × 51 615 prime X15 27 × 3E
216 2 × 32 × 15 616 2 × 32 × 72 X16 2 × 36
217 prime 617 prime X17 prime
218 22 × 7 × E 618 22 × 11 × 15 X18 22 × 5 × 61
219 3 × 87 619 3 × 5 × 4E X19 3 × 347
21X 2 × 5 × 27 61X 2 × 30E X1X 2 × 15 × 37
21E prime 61E prime X1E 7 × E × 17
220 23 × 3 × 11 620 23 × 3 × 31 X20 23 × 3 × 51
221 prime 621 7 × X7 X21 5 × 205
222 2 × 111 622 2 × 5 × 75 X22 2 × 511
223 32 × 5 × 7 623 34 × E X23 32 × 117
224 22 × 67 624 22 × 167 X24 22 × 267
225 prime 625 17 × 3E X25 11 × 95
226 2 × 3 × 45 626 2 × 3 × 105 X26 2 × 3 × 5 × 72
227 E × 25 627 5 × 12E X27 prime
228 26 × 5 628 27 × 7 X28 26 × 1E
229 3 × 8E 629 3 × 11 × 1E X29 3 × 34E
22X 2 × 7 × 1E 62X 2 × 315 X2X 2 × E × 57
22E 15 × 17 62E 25 × 27 X2E 52 × 4E
230 22 × 34 630 22 × 32 × 52 X30 22 × 32 × 35
231 52 × 11 631 15 × 45 X31 7 × 157
232 2 × 117 632 2 × E × 35 X32 2 × 517
233 3 × 91 633 3 × 7 × 37 X33 3 × 15 × 25
234 23 × 35 634 23 × 95 X34 23 × 5 × 31
235 7 × 3E 635 5 × 131 X35 prime
236 2 × 3 × 5 × E 636 2 × 3 × 107 X36 2 × 3 × 11 × 17
237 prime 637 prime X37 prime
238 22 × 6E 638 22 × 16E X38 22 × 7 × 45
239 32 × 31 639 32 × 85 X39 33 × 5 × E
23X 2 × 11E 63X 2 × 5 × 7 × 11 X3X 2 × 51E
23E 5 × 57 63E prime X3E prime
240 24 × 3 × 7 640 24 × 3 × 17 X40 24 × 3 × 27
241 prime 641 E × 6E X41 prime
242 2 × 112 642 2 × 321 X42 2 × 5 × 105
243 3 × 95 643 3 × 5 × 51 X43 3 × 7 × 5E
244 22 × 5 × 15 644 22 × 171 X44 22 × 271
245 E × 27 645 7 × XE X45 prime
246 2 × 32 × 17 646 2 × 33 × 15 X46 2 × 32 × 6E
247 73 647 prime X47 5 × 11 × 1E
248 23 × 37 648 23 × 5 × 1E X48 23 × E × 15
249 3 × 5 × 1E 649 3 × 217 X49 3 × 357
24X 2 × 125 64X 2 × 325 X4X 2 × 7 × 8E
24E prime 64E 11 × 5E X4E prime
250 22 × 3 × 25 650 22 × 3 × 7 × E X50 22 × 3 × 53
251 prime 651 52 × 31 X51 17 × 67
252 2 × 52 × 7 652 2 × 327 X52 2 × 527
253 33 × 11 653 32 × 87 X53 32 × 11E
254 25 × E 654 25 × 25 X54 25 × 3E
255 prime 655 prime X55 5 × 7 × 37
256 2 × 3 × 4E 656 2 × 3 × 5 × 27 X56 2 × 3 × 18E
257 5 × 5E 657 72 × 17 X57 E × E5
258 22 × 75 658 22 × 175 X58 22 × 11 × 25
259 3 × 7 × 15 659 3 × 21E X59 3 × 35E
25X 2 × 12E 65X 2 × 32E X5X 2 × 5 × 107
25E prime 65E 5 × E × 15 X5E prime
260 23 × 32 × 5 660 23 × 32 × 11 X60 23 × 33 × 7
261 172 661 prime X61 15 × 75
262 2 × 131 662 2 × 7 × 57 X62 2 × 531
263 3 × E2 663 3 × 221 X63 3 × 5 × 85
264 22 × 7 × 11 664 22 × 5 × 3E X64 22 × 277
265 5 × 61 665 prime X65 31 × 35
266 2 × 3 × 51 666 2 × 3 × 111 X66 2 × 3 × E × 1E
267 prime 667 1E × 35 X67 72 × 27
268 24 × 1E 668 24 × 4E X68 24 × 5 × 17
269 32 × 35 669 33 × 5 × 7 X69 32 × 112
26X 2 × 5 × 31 66X 2 × E × 37 X6X 2 × 535
26E 7 × 45 66E prime X6E prime
270 22 × 3 × 27 670 22 × 3 × 67 X70 22 × 3 × X7
271 prime 671 11 × 61 X71 52 × 51
272 2 × E × 15 672 2 × 52 × 17 X72 2 × 7 × 91
273 3 × 53 673 3 × 225 X73 3 × 365
274 23 × 3E 674 23 × 7 × 15 X74 23 × 13E
275 11 × 25 675 prime X75 E × E7
276 2 × 33 × 7 676 2 × 32 × 45 X76 2 × 32 × 5 × 15
277 prime 677 5 × 13E X77 prime
278 22 × 5 × 17 678 22 × 17E X78 22 × 27E
279 3 × X7 679 3 × E × 25 X79 3 × 7 × 61
27X 2 × 13E 67X 2 × 33E X7X 2 × 11 × 4E
27E prime 67E 7 × E5 X7E 5 × 217
280 27 × 3 680 26 × 3 × 5 X80 29 × 3
281 5 × 7 × E 681 272 X81 25 × 45
282 2 × 141 682 2 × 11 × 31 X82 2 × 541
283 32 × 37 683 32 × 8E X83 34 × 17
284 22 × 81 684 22 × 181 X84 22 × 5 × 7 × E
285 prime 685 5 × 141 X85 1E × 57
286 2 × 3 × 5 × 11 686 2 × 3 × 7 × 1E X86 2 × 3 × 195
287 15 × 1E 687 prime X87 prime
288 23 × 72 688 23 × E2 X88 23 × 141
289 3 × XE 689 3 × 15 × 17 X89 3 × 5 × 87
28X 2 × 145 68X 2 × 5 × 81 X8X 2 × 545
28E 5 × 67 68E prime X8E 7 × 11 × 15
290 22 × 32 × E 690 22 × 35 X90 22 × 32 × 37
291 prime 691 7 × E7 X91 prime
292 2 × 147 692 2 × 347 X92 2 × 52 × 27
293 3 × 7 × 17 693 3 × 52 × 11 X93 3 × E × 3E
294 24 × 52 694 24 × 51 X94 24 × 81
295 prime 695 prime X95 prime
296 2 × 3 × 57 696 2 × 3 × 117 X96 2 × 3 × 7 × 31
297 11 × 27 697 E × 75 X97 5 × 21E
298 22 × 85 698 22 × 5 × 72 X98 22 × 285
299 34 × 5 699 32 × 91 X99 32 × 125
29X 2 × 7 × 25 69X 2 × 34E X9X 2 × 17 × 35
29E E × 31 69E prime X9E prime
2X0 23 × 3 × 15 6X0 23 × 3 × 35 XX0 23 × 3 × 5 × 11
2X1 prime 6X1 5 × 145 XX1 7 × 167
2X2 2 × 5 × 35 6X2 2 × 15 × 25 XX2 2 × E × 5E
2X3 3 × E5 6X3 3 × 7 × 3E XX3 3 × 375
2X4 22 × 87 6X4 22 × 11 × 17 XX4 22 × 15 × 1E
2X5 7 × 4E 6X5 1E × 37 XX5 5 × 221
2X6 2 × 32 × 1E 6X6 2 × 32 × 5 × E XX6 2 × 33 × 25
2X7 5 × 6E 6X7 prime XX7 prime
2X8 25 × 11 6X8 25 × 27 XX8 25 × 72
2X9 3 × E7 6X9 3 × 237 XX9 3 × 377
2XX 2 × E × 17 6XX 2 × 7 × 5E XXX 2 × 5 × 111
2XE prime 6XE 5 × 147 XXE prime
2E0 22 × 3 × 5 × 7 6E0 22 × 3 × 6E XE0 22 × 3 × XE
2E1 prime 6E1 prime XE1 E2 × 11
2E2 2 × 157 6E2 2 × 357 XE2 2 × 557
2E3 32 × 3E 6E3 33 × 31 XE3 32 × 52 × 7
2E4 23 × 45 6E4 23 × 53 XE4 23 × 145
2E5 52 × 15 6E5 7 × E × 11 XE5 17 × 6E
2E6 2 × 3 × 5E 6E6 2 × 3 × 11E XE6 2 × 3 × 19E
2E7 7 × 51 6E7 15 × 4E XE7 prime
2E8 22 × 8E 6E8 22 × 18E XE8 22 × 5 × 67
2E9 3 × E × 11 6E9 3 × 5 × 57 XE9 3 × 15 × 27
2EX 2 × 5 × 37 6EX 2 × 35E XEX 2 × 7 × 95
2EE prime 6EE 17 × 45 XEE prime
300 24 × 33 700 24 × 32 × 7 E00 24 × 32 × E
301 prime 701 prime E01 5 × 225
302 2 × 7 × 27 702 2 × 5 × 85 E02 2 × 11 × 51
303 3 × 5 × 25 703 3 × 241 E03 3 × 1E2
304 22 × 91 704 22 × E × 1E E04 22 × 291
305 17 × 1E 705 prime E05 7 × 16E
306 2 × 3 × 61 706 2 × 3 × 112 E06 2 × 3 × 5 × 45
307 prime 707 5 × 7 × 25 E07 31 × 37
308 23 × 5 × E 708 23 × X7 E08 23 × 147
309 32 × 72 709 32 × 95 E09 33 × 4E
30X 2 × 11 × 15 70X 2 × 365 E0X 2 × 565
30E prime 70E prime E0E 5 × E × 25
310 22 × 3 × 31 710 22 × 3 × 5 × 15 E10 22 × 3 × 7 × 17
311 5 × 75 711 prime E11 prime
312 2 × 167 712 2 × 7 × 61 E12 2 × 15 × 3E
313 3 × 105 713 3 × E × 27 E13 3 × 11 × 35
314 26 × 7 714 2X E14 26 × 52
315 prime 715 52 × 35 E15 prime
316 2 × 32 × 52 716 2 × 33 × 17 E16 2 × 32 × 75
317 E × 35 717 11 × 67 E17 7 × 171
318 22 × 95 718 22 × 195 E18 22 × 295
319 3 × 107 719 3 × 73 E19 3 × 5 × 8E
31X 2 × 16E 71X 2 × 5 × 87 E1X 2 × E × 61
31E 5 × 7 × 11 71E prime E1E prime
320 23 × 3 × 17 720 23 × 3 × 37 E20 23 × 3 × 57
321 prime 721 prime E21 prime
322 2 × 171 722 2 × E × 3E E22 2 × 5 × 7 × 1E
323 33 × 15 723 32 × 5 × 1E E23 32 × 12E
324 22 × 5 × 1E 724 22 × 7 × 31 E24 22 × 11 × 27
325 prime 725 15 × 51 E25 prime
326 2 × 3 × 7 × E 726 2 × 3 × 125 E26 2 × 3 × 1X5
327 prime 727 prime E27 5 × 15 × 17
328 24 × 25 728 24 × 5 × 11 E28 24 × 85
329 3 × 5 × 27 729 3 × 24E E29 3 × 72 × E
32X 2 × 175 72X 2 × 375 E2X 2 × 575
32E prime 72E 7 × 105 E2E prime
330 22 × 32 × 11 730 22 × 32 × 25 E30 22 × 34 × 5
331 7 × 57 731 5 × E × 17 E31 prime
332 2 × 5 × 3E 732 2 × 377 E32 2 × 577
333 3 × 111 733 3 × 251 E33 3 × 391
334 23 × 4E 734 23 × XE E34 23 × 7 × 25
335 E × 37 735 prime E35 53 × 11
336 2 × 3 × 67 736 2 × 3 × 52 × 7 E36 2 × 3 × 1X7
337 52 × 17 737 prime E37 prime
338 22 × 7 × 15 738 22 × 19E E38 22 × E × 31
339 32 × 45 739 34 × 11 E39 32 × 131
33X 2 × 17E 73X 2 × 15 × 27 E3X 2 × 5 × 117
33E prime 73E 5 × 157 E3E 7 × 175
340 25 × 3 × 5 740 25 × 3 × E E40 25 × 3 × 15
341 11 × 31 741 7 × 107 E41 1E × 5E
342 2 × 181 742 2 × 1E2 E42 2 × 17 × 37
343 3 × 7 × 1E 743 3 × 255 E43 3 × 5 × 91
344 22 × E2 744 22 × 5 × 45 E44 22 × 2X1
345 5 × 81 745 prime E45 prime
346 2 × 35 746 2 × 32 × 4E E46 2 × 32 × 7 × 11
347 prime 747 prime E47 E × 105
348 23 × 51 748 23 × 7 × 17 E48 23 × 5 × 35
349 3 × 117 749 3 × 5 × 5E E49 3 × 397
34X 2 × 5 × 72 74X 2 × 11 × 35 E4X 2 × 585
34E prime 74E E × 81 E4E 27 × 45
350 22 × 3 × 35 750 22 × 3 × 75 E50 22 × 3 × E5
351 15 × 25 751 prime E51 5 × 7 × 3E
352 2 × 11 × 17 752 2 × 5 × 8E E52 2 × 587
353 32 × 5 × E 753 32 × 7 × 15 E53 33 × 51
354 24 × 27 754 24 × 57 E54 24 × 87
355 7 × 5E 755 25 × 31 E55 15 × 81
356 2 × 3 × 6E 756 2 × 3 × 12E E56 2 × 3 × 52 × E
357 prime 757 52 × 37 E57 11 × X7
358 22 × 53 758 22 × 1X5 E58 22 × 7 × 4E
359 3 × 11E 759 3 × 25E E59 3 × 17 × 25
35X 2 × 18E 75X 2 × 72 × E E5X 2 × 58E
35E prime 75E 11 × 6E E5E 5 × 237
360 23 × 32 × 7 760 23 × 33 × 5 E60 23 × 32 × 1E
361 5 × 85 761 1E × 3E E61 prime
362 2 × E × 1E 762 2 × 391 E62 2 × 591
363 3 × 112 763 3 × 172 E63 3 × 7 × 67
364 22 × X7 764 22 × 1X7 E64 22 × 5 × 6E
365 prime 765 5 × 7 × 27 E65 E × 107
366 2 × 3 × 5 × 15 766 2 × 3 × 131 E66 2 × 3 × 1E1
367 7 × 61 767 prime E67 prime
368 29 768 26 × 15 E68 27 × 11
369 33 × 17 769 32 × E2 E69 32 × 5 × 31
36X 2 × 195 76X 2 × 5 × 91 E6X 2 × 72 × 15
36E 5 × 87 76E prime E6E prime
370 22 × 3 × 37 770 22 × 3 × 7 × 11 E70 22 × 3 × E7
371 E × 3E 771 prime E71 prime
372 2 × 7 × 31 772 2 × 397 E72 2 × 5 × 11E
373 3 × 125 773 3 × 5 × 61 E73 3 × 3X5
374 23 × 5 × 11 774 23 × E5 E74 23 × E × 17
375 prime 775 prime E75 7 × 17E
376 2 × 32 × 25 776 2 × 32 × 51 E76 2 × 33 × 27
377 prime 777 7 × 111 E77 52 × 57
378 22 × XE 778 22 × 52 × E E78 22 × 2XE
379 3 × 52 × 7 779 3 × 267 E79 3 × 11 × 37
37X 2 × 19E 77X 2 × 17 × 25 E7X 2 × 59E
37E 15 × 27 77E prime E7E 1E × 61
380 24 × 3 × E 780 24 × 3 × 1E E80 24 × 3 × 5 × 7
381 1E2 781 5 × 11 × 15 E81 352
382 2 × 5 × 45 782 2 × 7 × 67 E82 2 × 252
383 32 × 4E 783 33 × 35 E83 32 × E × 15
384 22 × 7 × 17 784 22 × 1E1 E84 22 × 2E1
385 11 × 35 785 prime E85 5 × 241
386 2 × 3 × 75 786 2 × 3 × 5 × 31 E86 2 × 3 × 1E5
387 5 × 8E 787 E × 85 E87 7 × 181
388 23 × 57 788 23 × E7 E88 23 × 157
389 3 × 12E 789 3 × 7 × 45 E89 3 × 3XE
38X 2 × 1X5 78X 2 × 3X5 E8X 2 × 5 × 112
38E 72 × E 78E 5 × 167 E8E 17 × 75
390 22 × 33 × 5 790 22 × 32 × 27 E90 22 × 32 × 3E
391 prime 791 prime E91 prime
392 2 × 1X7 792 2 × 11 × 37 E92 2 × 7 × E2
393 3 × 131 793 3 × 271 E93 3 × 5 × 95
394 25 × 15 794 25 × 5 × 7 E94 25 × 45
395 5 × 91 795 17 × 4E E95 prime
396 2 × 3 × 7 × 11 796 2 × 3 × E × 15 E96 2 × 3 × 1E7
397 prime 797 prime E97 prime
398 22 × E5 798 22 × 1E5 E98 22 × 52 × 15
399 32 × 51 799 32 × 53 E99 35 × 7
39X 2 × 52 × E 79X 2 × 3XE E9X 2 × 1E × 31
39E 17 × 25 79E 72 × 1E E9E 11 × XE
3X0 23 × 3 × 1E 7X0 23 × 3 × 3E EX0 23 × 3 × 5E
3X1 7 × 67 7X1 prime EX1 5 × E × 27
3X2 2 × 1E1 7X2 2 × 5 × 95 EX2 2 × 5E1
3X3 3 × 5 × 31 7X3 3 × 11 × 25 EX3 3 × 3E5
3X4 22 × E7 7X4 22 × 1E7 EX4 22 × 7 × 51
3X5 prime 7X5 E × 87 EX5 prime
3X6 2 × 32 × 27 7X6 2 × 34 × 7 EX6 2 × 32 × 5 × 17
3X7 11 × 37 7X7 5 × 16E EX7 25 × 4E
3X8 24 × 5 × 7 7X8 24 × 5E EX8 24 × 8E
3X9 3 × E × 15 7X9 3 × 277 EX9 3 × 3E7
3XX 2 × 1E5 7XX 2 × 3E5 EXX 2 × 5E5
3XE prime 7XE 15 × 57 EXE 5 × 73
3E0 22 × 3 × 3E 7E0 22 × 3 × 5 × 17 EE0 22 × 3 × E × 11
3E1 5 × 95 7E1 7 × 117 EE1 15 × 85
3E2 2 × 1E7 7E2 2 × 3E7 EE2 2 × 5E7
3E3 34 × 7 7E3 32 × X7 EE3 32 × 13E
3E4 23 × 5E 7E4 23 × E × 11 EE4 23 × 5 × 37
3E5 prime 7E5 5 × 171 EE5 prime
3E6 2 × 3 × 5 × 17 7E6 2 × 3 × 13E EE6 2 × 3 × 7 × 35
3E7 prime 7E7 27 × 31 EE7 prime
3E8 22 × E × 11 7E8 22 × 7 × 35 EE8 22 × 2EE
3E9 3 × 13E 7E9 3 × 27E EE9 3 × 52 × 1E
3EX 2 × 7 × 35 7EX 2 × 52 × 1E EEX 2 × 5EE
3EE 52 × 1E 7EE prime EEE E × 111
400 26 × 32 800 27 × 32 1000 26 × 33