What are the divisors of 2656?

1, 2, 4, 8, 16, 32, 83, 166, 332, 664, 1328, 2656

There is a total of 12 positive divisors.
The sum of these divisors is 5292.
The arithmetic mean is 441.

10 even divisors

2, 4, 8, 16, 32, 166, 332, 664, 1328, 2656

2 odd divisors

1, 83

How to compute the divisors of 2656?

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 2656 by each of the numbers from 1 to 2656 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)

2656 / 1 = 2656 (the remainder is 0, so 1 is a divisor of 2656)
2656 / 2 = 1328 (the remainder is 0, so 2 is a divisor of 2656)
2656 / 3 = 885.33333333333 (the remainder is 1, so 3 is not a divisor of 2656)
...
2656 / 2655 = 1.0003766478343 (the remainder is 1, so 2655 is not a divisor of 2656)
2656 / 2656 = 1 (the remainder is 0, so 2656 is a divisor of 2656)

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 2656 (i.e. 51.536394906901). 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 $\frac{N}{d} = D$ )

2656 / 1 = 2656 (the remainder is 0, so 1 and 2656 are divisors of 2656)
2656 / 2 = 1328 (the remainder is 0, so 2 and 1328 are divisors of 2656)
2656 / 3 = 885.33333333333 (the remainder is 1, so 3 is not a divisor of 2656)
...
2656 / 50 = 53.12 (the remainder is 6, so 50 is not a divisor of 2656)
2656 / 51 = 52.078431372549 (the remainder is 4, so 51 is not a divisor of 2656)