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Divisor
 For the second operand of a division, see division (mathematics).
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. The statement "m is a divisor of n" can be written as [math]m \mid n[/math].^{[1]}^{[2]} Any number is always evenly divisible by 1 and itself, which are two of the divisors. A prime number is a number with no other divisors. The positive divisors of a number n, other than n itself, are the proper divisors of n.^{[3]}
Finding one or more factors of a given number is called factorization.
Explanation
For example, 7 is a divisor of 42 because 42÷7 = 6. We also say that "42 is divisible by 7", "42 is a multiple of 7", "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 that m divides n for nonzero integers m and n, if and only if there exists an integer k such that n = km. Thus, divisors can be negative as well as positive, although we often 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.)
1 and 1 divide (are divisors of) every integer, every integer is a divisor of itself, and every integer is a divisor of 0, except by convention 0 itself (see also Division by zero). Numbers divisible by 2 are called even, and numbers not divisible by 2 are called odd.
A divisor of n that is not 1, 1, n or n is known as a nontrivial divisor; numbers with nontrivial divisors are known as composite numbers, while prime numbers have no nontrivial divisors.
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.
Spotting divisors
There are properties which allow one to recognize certain divisors of a number from the number's digits. Those properties can be used as "math tricks" to quickly spot some divisors of a number.
For example, if the last digit is even (0, 2, 4, 6 or 8), then 2 is a divisor. If the last digit is 0 or 5, then 5 is a divisor. If the digits add up to a multiple of 3, then 3 is a divisor. For the number 340, ending in "0" then both 2 and 5 are divisors, plus 2×5 = 10 is also a divisor. Dividing by 10, 340/10 = 34, as finally 2×17. Combining all the smaller numbers, the 12 divisors of 340 are:
 Divisors of 340: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340.
Note that any number is always evenly divisible by 1 and itself.
Related pages
References
 ↑ "Compendium of Mathematical Symbols" (in enUS). 20200301. https://mathvault.ca/hub/highermath/mathsymbols/.
 ↑ Weisstein, Eric W.. "Divisor" (in en). https://mathworld.wolfram.com/Divisor.html.
 ↑ Caldwell, Chris. "Divisor". https://primes.utm.edu/glossary/page.php?sort=Divisor.
Other websites
 Online Number Factorizer Instantly factors numbers up to 17 digits long
 Factoring Calculator  Factoring calculator that displays the prime factors and the prime and nonprime divisors of a given number.
