What are the divisors of 920?

1, 2, 4, 5, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920

There is a total of 16 positive divisors.
The sum of these divisors is 2160.
The arithmetic mean is 135.

12 even divisors

2, 4, 8, 10, 20, 40, 46, 92, 184, 230, 460, 920

4 odd divisors

1, 5, 23, 115

How to compute the divisors of 920?

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 920 by each of the numbers from 1 to 920 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)

920 / 1 = 920 (the remainder is 0, so 1 is a divisor of 920)
920 / 2 = 460 (the remainder is 0, so 2 is a divisor of 920)
920 / 3 = 306.66666666667 (the remainder is 2, so 3 is not a divisor of 920)
...
920 / 919 = 1.0010881392818 (the remainder is 1, so 919 is not a divisor of 920)
920 / 920 = 1 (the remainder is 0, so 920 is a divisor of 920)

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 920 (i.e. 30.331501776206). 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 $\frac{N}{d} = D$ )

920 / 1 = 920 (the remainder is 0, so 1 and 920 are divisors of 920)
920 / 2 = 460 (the remainder is 0, so 2 and 460 are divisors of 920)
920 / 3 = 306.66666666667 (the remainder is 2, so 3 is not a divisor of 920)
...
920 / 29 = 31.724137931034 (the remainder is 21, so 29 is not a divisor of 920)
920 / 30 = 30.666666666667 (the remainder is 20, so 30 is not a divisor of 920)