What are the divisors of 928?

1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928

There is a total of 12 positive divisors.
The sum of these divisors is 1890.
The arithmetic mean is 157.5.

10 even divisors

2, 4, 8, 16, 32, 58, 116, 232, 464, 928

2 odd divisors

1, 29

How to compute the divisors of 928?

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 928 by each of the numbers from 1 to 928 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)

928 / 1 = 928 (the remainder is 0, so 1 is a divisor of 928)
928 / 2 = 464 (the remainder is 0, so 2 is a divisor of 928)
928 / 3 = 309.33333333333 (the remainder is 1, so 3 is not a divisor of 928)
...
928 / 927 = 1.0010787486516 (the remainder is 1, so 927 is not a divisor of 928)
928 / 928 = 1 (the remainder is 0, so 928 is a divisor of 928)

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 928 (i.e. 30.463092423456). 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 $\frac{N}{d} = D$ )

928 / 1 = 928 (the remainder is 0, so 1 and 928 are divisors of 928)
928 / 2 = 464 (the remainder is 0, so 2 and 464 are divisors of 928)
928 / 3 = 309.33333333333 (the remainder is 1, so 3 is not a divisor of 928)
...
928 / 29 = 32 (the remainder is 0, so 29 and 32 are divisors of 928)
928 / 30 = 30.933333333333 (the remainder is 28, so 30 is not a divisor of 928)