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Divisors

Divisors of 5040

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520 and 5040

About Divisors

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 5040 is divisible by a total of 60 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.