Divisor

:For divisors in algebraic geometry, see divisor (algebraic geometry).

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In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. For example, 7 is a divisor of 42 because 42/7 = 6. We also say 42 is divisible by 7 or 42 is a multiple of 7 or 7 divides 42 and we usually write 7 | 42. For example, the positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

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In general, we say m|n (read: m divides n) for any integers m and n iff there exists an integer k such that n = km. Thus, divisors can be negative as well as positive. 1 and -1 are divisors of every integer, every integer is a divisor of itself, and every integer is a divisor of 0, while 0 is a divisor only of 0 (see also division by zero). Numbers divisible by 2 are called even and those that are not are called odd.

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A divisor of n that is not 1, -1, n or -n is known as a non-trivial divisor; numbers with non-trivial divisors are known as composite numbers, while prime numbers have no non-trivial divisors.

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The name comes from the arithmetic operation of division: if a/b=c then a is the dividend, b the divisor, and c the quotient.

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There are some rules which allow to recognize small divisors of a number from the number's decimal digits.

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Integer: The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. The set of all integers is usually denoted in mathematics by Z (or Z in blackboard bold, mathbb{Z}), which stands for Zahlen (German for "numbers"). The...

Remainder: In mathematics, the result of the division of two integers usually cannot be expressed with an integer quotient, unless a remainder —an amount "left over"— is also acknowledged....

Iff: IFF, Iff or iff can stand for:...