What are the divisors of 5664?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 59, 96, 118, 177, 236, 354, 472, 708, 944, 1416, 1888, 2832, 5664

There is a total of 24 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 630.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 96, 118, 236, 354, 472, 708, 944, 1416, 1888, 2832, 5664

4 odd divisors

1, 3, 59, 177

How to compute the divisors of 5664?

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 5664 by each of the numbers from 1 to 5664 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)

5664 / 1 = 5664 (the remainder is 0, so 1 is a divisor of 5664)
5664 / 2 = 2832 (the remainder is 0, so 2 is a divisor of 5664)
5664 / 3 = 1888 (the remainder is 0, so 3 is a divisor of 5664)
...
5664 / 5663 = 1.000176584849 (the remainder is 1, so 5663 is not a divisor of 5664)
5664 / 5664 = 1 (the remainder is 0, so 5664 is a divisor of 5664)

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 5664 (i.e. 75.259550888907). 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 $\frac{N}{d} = D$ )

5664 / 1 = 5664 (the remainder is 0, so 1 and 5664 are divisors of 5664)
5664 / 2 = 2832 (the remainder is 0, so 2 and 2832 are divisors of 5664)
5664 / 3 = 1888 (the remainder is 0, so 3 and 1888 are divisors of 5664)
...
5664 / 74 = 76.540540540541 (the remainder is 40, so 74 is not a divisor of 5664)
5664 / 75 = 75.52 (the remainder is 39, so 75 is not a divisor of 5664)