What are the divisors of 2976?

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

There is a total of 24 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 336.

20 even divisors

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

4 odd divisors

1, 3, 31, 93

How to compute the divisors of 2976?

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 2976 by each of the numbers from 1 to 2976 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)

2976 / 1 = 2976 (the remainder is 0, so 1 is a divisor of 2976)
2976 / 2 = 1488 (the remainder is 0, so 2 is a divisor of 2976)
2976 / 3 = 992 (the remainder is 0, so 3 is a divisor of 2976)
...
2976 / 2975 = 1.0003361344538 (the remainder is 1, so 2975 is not a divisor of 2976)
2976 / 2976 = 1 (the remainder is 0, so 2976 is a divisor of 2976)

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 2976 (i.e. 54.552726787943). 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 $\frac{N}{d} = D$ )

2976 / 1 = 2976 (the remainder is 0, so 1 and 2976 are divisors of 2976)
2976 / 2 = 1488 (the remainder is 0, so 2 and 1488 are divisors of 2976)
2976 / 3 = 992 (the remainder is 0, so 3 and 992 are divisors of 2976)
...
2976 / 53 = 56.150943396226 (the remainder is 8, so 53 is not a divisor of 2976)
2976 / 54 = 55.111111111111 (the remainder is 6, so 54 is not a divisor of 2976)