What are the divisors of 912?

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 114, 152, 228, 304, 456, 912

There is a total of 20 positive divisors.
The sum of these divisors is 2480.
The arithmetic mean is 124.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 38, 48, 76, 114, 152, 228, 304, 456, 912

4 odd divisors

1, 3, 19, 57

How to compute the divisors of 912?

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 912 by each of the numbers from 1 to 912 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)

912 / 1 = 912 (the remainder is 0, so 1 is a divisor of 912)
912 / 2 = 456 (the remainder is 0, so 2 is a divisor of 912)
912 / 3 = 304 (the remainder is 0, so 3 is a divisor of 912)
...
912 / 911 = 1.0010976948408 (the remainder is 1, so 911 is not a divisor of 912)
912 / 912 = 1 (the remainder is 0, so 912 is a divisor of 912)

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 912 (i.e. 30.199337741083). 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 $\frac{N}{d} = D$ )

912 / 1 = 912 (the remainder is 0, so 1 and 912 are divisors of 912)
912 / 2 = 456 (the remainder is 0, so 2 and 456 are divisors of 912)
912 / 3 = 304 (the remainder is 0, so 3 and 304 are divisors of 912)
...
912 / 29 = 31.448275862069 (the remainder is 13, so 29 is not a divisor of 912)
912 / 30 = 30.4 (the remainder is 12, so 30 is not a divisor of 912)