An integer number B is a divisor of another integer A if A divided by B results in an integer, or expressed differently, if the remainder of the integer division of A and B is 0. In most programming languages, this is typically computed by the modulo operator, %, where B is a divisor of A if A % B == 0. For example, 4 is a divisor of 24, because 24 divided by 4 results in the integer 6. Programmatically, 24 % 4 == 0. Conversely, 5 is not a divisor of 24, since 24 divided by 5 results in 4.8, and the remainder is 24 % 5 == 4.

The Number of Divisors

The number 195 is divisible by a total of 8 divisors.

The divisors of an integer is made up of all unique permutations of its prime factorization. As a result, a number has more divisors the more prime factors it is made up of. To have the maximum amount of divisors, the prime factors of a number should be as small as possible, but also not too repetitive. A number which has more divisors than any smaller number, is called a highly composite number. A couple of examples include 60, 840, 5040, and 720720. The largest highly composite number on integers.info is 866421317361600, which has a total of 26880 divisors.