What are the divisors of 924?

1, 2, 3, 4, 6, 7, 11, 12, 14, 21, 22, 28, 33, 42, 44, 66, 77, 84, 132, 154, 231, 308, 462, 924

There is a total of 24 positive divisors.
The sum of these divisors is 2688.
The arithmetic mean is 112.

16 even divisors

2, 4, 6, 12, 14, 22, 28, 42, 44, 66, 84, 132, 154, 308, 462, 924

8 odd divisors

1, 3, 7, 11, 21, 33, 77, 231

How to compute the divisors of 924?

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 924 by each of the numbers from 1 to 924 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)

924 / 1 = 924 (the remainder is 0, so 1 is a divisor of 924)
924 / 2 = 462 (the remainder is 0, so 2 is a divisor of 924)
924 / 3 = 308 (the remainder is 0, so 3 is a divisor of 924)
...
924 / 923 = 1.0010834236186 (the remainder is 1, so 923 is not a divisor of 924)
924 / 924 = 1 (the remainder is 0, so 924 is a divisor of 924)

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 924 (i.e. 30.397368307141). 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 $\frac{N}{d} = D$ )

924 / 1 = 924 (the remainder is 0, so 1 and 924 are divisors of 924)
924 / 2 = 462 (the remainder is 0, so 2 and 462 are divisors of 924)
924 / 3 = 308 (the remainder is 0, so 3 and 308 are divisors of 924)
...
924 / 29 = 31.862068965517 (the remainder is 25, so 29 is not a divisor of 924)
924 / 30 = 30.8 (the remainder is 24, so 30 is not a divisor of 924)