What are the divisors of 2496?

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 156, 192, 208, 312, 416, 624, 832, 1248, 2496

There is a total of 28 positive divisors.
The sum of these divisors is 7112.
The arithmetic mean is 254.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 26, 32, 48, 52, 64, 78, 96, 104, 156, 192, 208, 312, 416, 624, 832, 1248, 2496

4 odd divisors

1, 3, 13, 39

How to compute the divisors of 2496?

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 2496 by each of the numbers from 1 to 2496 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)

2496 / 1 = 2496 (the remainder is 0, so 1 is a divisor of 2496)
2496 / 2 = 1248 (the remainder is 0, so 2 is a divisor of 2496)
2496 / 3 = 832 (the remainder is 0, so 3 is a divisor of 2496)
...
2496 / 2495 = 1.0004008016032 (the remainder is 1, so 2495 is not a divisor of 2496)
2496 / 2496 = 1 (the remainder is 0, so 2496 is a divisor of 2496)

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 2496 (i.e. 49.959983987187). 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 $\frac{N}{d} = D$ )

2496 / 1 = 2496 (the remainder is 0, so 1 and 2496 are divisors of 2496)
2496 / 2 = 1248 (the remainder is 0, so 2 and 1248 are divisors of 2496)
2496 / 3 = 832 (the remainder is 0, so 3 and 832 are divisors of 2496)
...
2496 / 48 = 52 (the remainder is 0, so 48 and 52 are divisors of 2496)
2496 / 49 = 50.938775510204 (the remainder is 46, so 49 is not a divisor of 2496)