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In mathematics, natural numbers are those used for counting and ordering.

Some authors begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, and others start with 1, corresponding to the positive integers 1, 2, 3, etc...

Properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics.

In mathematics, parity is the property of an integer of whether it is even or odd. 
An integer's parity is even if it is divisible by two with no remainders left, and its parity is odd if it isn't; that is, its remainder is 1.