divisor n
1. one of two or more integers that can be exactly divided into another integer; "what are the 4 factors of 6?" [syn: factor]
2. the number by which a dividend is divided

Divisor \Di*vi"sor\, n. [L., fr. dividere. See Divide.] (Math.) The number by which the dividend is divided. Common divisor. (Math.) See under Common, a.

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. Any number is always evenly divisible by 1 and itself, which are two of the divisors. A prime number has no other divisors.

Finding one or more factors of a given number is called factorization.

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 or 7 is a factor of 42 and we usually write 7 | 42. For example, the positive divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

In general, we say m|n (read: m divides n) for non-zero integers m and n iff there exists an integer k such that n = km. Thus, divisors can be negative as well as positive, although often we restrict our attention to positive divisors. (For example, there are six divisors of four, 1, 2, 4, -1, -2, -4, but one would usually mention only the positive ones, 1, 2, and 4.)

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