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Parity is defined to be the property of being even or odd. The parity of a number is even if the number is divisible by 2 with no remainder, a.k.a. its prime factorization contains the prime 2, is odd if the number is not divisible by 2, a.k.a. its prime factorization does not contain the prime 2.

For example, -6, 2, and 1X are even numbers because they can be divided by 2 with no remainder, while -9, -1, and 11 are odd numbers because they cannot be divided by 2 with no remainder.

Two numbers have the same parity if both are even or both are odd. Two numbers have opposite parity if one of them is even and the other one is odd. -2 and 6 have the same parity because they are both even, and -5 and E also have the same parity because they are both odd. -3 and 8 have opposite parities because -3 is odd and 8 is even.

The parity of zero is even. Note that parity cannot be applied to fractions and dozenals (like 1/2 and 3.5X02), they are neither even nor odd.

Operations on even and odd numbers[]

These operations are always true for any even number and any odd number, they are a special case for modular arithmetic. They are commonly used to check if an equation is correct or wrong.

Addition and subtraction[]

  • even ± even = even
  • even ± odd = odd
  • odd ± odd = even

Multiplication[]

  • even × even = even
  • even × odd = even
  • odd × odd = odd

Division[]

Dividing an integer by another integer does not always result in an integer, for example, 1 divided by 2 is equal to 1/2, which is a fraction, so it is neither even nor odd. However, when division does result in an integer value, the quotient will be even if the dividend has a higher power of 2 than the divisor and odd if the dividend has an equal power of 2 as the divisor.

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