What are the divisors of 5952?

1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 32, 48, 62, 64, 93, 96, 124, 186, 192, 248, 372, 496, 744, 992, 1488, 1984, 2976, 5952

There is a total of 28 positive divisors.
The sum of these divisors is 16256.
The arithmetic mean is 580.57142857143.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 62, 64, 96, 124, 186, 192, 248, 372, 496, 744, 992, 1488, 1984, 2976, 5952

4 odd divisors

1, 3, 31, 93

How to compute the divisors of 5952?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5952 by each of the numbers from 1 to 5952 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5952 / 1 = 5952 (the remainder is 0, so 1 is a divisor of 5952)
5952 / 2 = 2976 (the remainder is 0, so 2 is a divisor of 5952)
5952 / 3 = 1984 (the remainder is 0, so 3 is a divisor of 5952)
...
5952 / 5951 = 1.000168038985 (the remainder is 1, so 5951 is not a divisor of 5952)
5952 / 5952 = 1 (the remainder is 0, so 5952 is a divisor of 5952)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5952 (i.e. 77.149206087944). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5952 / 1 = 5952 (the remainder is 0, so 1 and 5952 are divisors of 5952)
5952 / 2 = 2976 (the remainder is 0, so 2 and 2976 are divisors of 5952)
5952 / 3 = 1984 (the remainder is 0, so 3 and 1984 are divisors of 5952)
...
5952 / 76 = 78.315789473684 (the remainder is 24, so 76 is not a divisor of 5952)
5952 / 77 = 77.298701298701 (the remainder is 23, so 77 is not a divisor of 5952)