What are the divisors of 4992?

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 312, 384, 416, 624, 832, 1248, 1664, 2496, 4992

There is a total of 32 positive divisors.
The sum of these divisors is 14280.
The arithmetic mean is 446.25.

28 even divisors

2, 4, 6, 8, 12, 16, 24, 26, 32, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 312, 384, 416, 624, 832, 1248, 1664, 2496, 4992

4 odd divisors

1, 3, 13, 39

How to compute the divisors of 4992?

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 4992 by each of the numbers from 1 to 4992 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)

4992 / 1 = 4992 (the remainder is 0, so 1 is a divisor of 4992)
4992 / 2 = 2496 (the remainder is 0, so 2 is a divisor of 4992)
4992 / 3 = 1664 (the remainder is 0, so 3 is a divisor of 4992)
...
4992 / 4991 = 1.0002003606492 (the remainder is 1, so 4991 is not a divisor of 4992)
4992 / 4992 = 1 (the remainder is 0, so 4992 is a divisor of 4992)

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 4992 (i.e. 70.654086930623). 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 $\frac{N}{d} = D$ )

4992 / 1 = 4992 (the remainder is 0, so 1 and 4992 are divisors of 4992)
4992 / 2 = 2496 (the remainder is 0, so 2 and 2496 are divisors of 4992)
4992 / 3 = 1664 (the remainder is 0, so 3 and 1664 are divisors of 4992)
...
4992 / 69 = 72.347826086957 (the remainder is 24, so 69 is not a divisor of 4992)
4992 / 70 = 71.314285714286 (the remainder is 22, so 70 is not a divisor of 4992)