What are the divisors of 2964?

1, 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, 1482, 2964

There is a total of 24 positive divisors.
The sum of these divisors is 7840.
The arithmetic mean is 326.66666666667.

16 even divisors

2, 4, 6, 12, 26, 38, 52, 76, 78, 114, 156, 228, 494, 988, 1482, 2964

8 odd divisors

1, 3, 13, 19, 39, 57, 247, 741

How to compute the divisors of 2964?

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 2964 by each of the numbers from 1 to 2964 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)

2964 / 1 = 2964 (the remainder is 0, so 1 is a divisor of 2964)
2964 / 2 = 1482 (the remainder is 0, so 2 is a divisor of 2964)
2964 / 3 = 988 (the remainder is 0, so 3 is a divisor of 2964)
...
2964 / 2963 = 1.0003374957813 (the remainder is 1, so 2963 is not a divisor of 2964)
2964 / 2964 = 1 (the remainder is 0, so 2964 is a divisor of 2964)

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 2964 (i.e. 54.442630355265). 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 $\frac{N}{d} = D$ )

2964 / 1 = 2964 (the remainder is 0, so 1 and 2964 are divisors of 2964)
2964 / 2 = 1482 (the remainder is 0, so 2 and 1482 are divisors of 2964)
2964 / 3 = 988 (the remainder is 0, so 3 and 988 are divisors of 2964)
...
2964 / 53 = 55.924528301887 (the remainder is 49, so 53 is not a divisor of 2964)
2964 / 54 = 54.888888888889 (the remainder is 48, so 54 is not a divisor of 2964)