What are the divisors of 656?

1, 2, 4, 8, 16, 41, 82, 164, 328, 656

There is a total of 10 positive divisors.
The sum of these divisors is 1302.
The arithmetic mean is 130.2.

8 even divisors

2, 4, 8, 16, 82, 164, 328, 656

2 odd divisors

1, 41

How to compute the divisors of 656?

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 656 by each of the numbers from 1 to 656 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)

656 / 1 = 656 (the remainder is 0, so 1 is a divisor of 656)
656 / 2 = 328 (the remainder is 0, so 2 is a divisor of 656)
656 / 3 = 218.66666666667 (the remainder is 2, so 3 is not a divisor of 656)
...
656 / 655 = 1.0015267175573 (the remainder is 1, so 655 is not a divisor of 656)
656 / 656 = 1 (the remainder is 0, so 656 is a divisor of 656)

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 656 (i.e. 25.612496949731). 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 $\frac{N}{d} = D$ )

656 / 1 = 656 (the remainder is 0, so 1 and 656 are divisors of 656)
656 / 2 = 328 (the remainder is 0, so 2 and 328 are divisors of 656)
656 / 3 = 218.66666666667 (the remainder is 2, so 3 is not a divisor of 656)
...
656 / 24 = 27.333333333333 (the remainder is 8, so 24 is not a divisor of 656)
656 / 25 = 26.24 (the remainder is 6, so 25 is not a divisor of 656)