What are the divisors of 5088?

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 53, 96, 106, 159, 212, 318, 424, 636, 848, 1272, 1696, 2544, 5088

There is a total of 24 positive divisors.
The sum of these divisors is 13608.
The arithmetic mean is 567.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 48, 96, 106, 212, 318, 424, 636, 848, 1272, 1696, 2544, 5088

4 odd divisors

1, 3, 53, 159

How to compute the divisors of 5088?

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 5088 by each of the numbers from 1 to 5088 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)

5088 / 1 = 5088 (the remainder is 0, so 1 is a divisor of 5088)
5088 / 2 = 2544 (the remainder is 0, so 2 is a divisor of 5088)
5088 / 3 = 1696 (the remainder is 0, so 3 is a divisor of 5088)
...
5088 / 5087 = 1.0001965795164 (the remainder is 1, so 5087 is not a divisor of 5088)
5088 / 5088 = 1 (the remainder is 0, so 5088 is a divisor of 5088)

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 5088 (i.e. 71.330218000508). 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 $\frac{N}{d} = D$ )

5088 / 1 = 5088 (the remainder is 0, so 1 and 5088 are divisors of 5088)
5088 / 2 = 2544 (the remainder is 0, so 2 and 2544 are divisors of 5088)
5088 / 3 = 1696 (the remainder is 0, so 3 and 1696 are divisors of 5088)
...
5088 / 70 = 72.685714285714 (the remainder is 48, so 70 is not a divisor of 5088)
5088 / 71 = 71.661971830986 (the remainder is 47, so 71 is not a divisor of 5088)