What are the divisors of 908?

1, 2, 4, 227, 454, 908

There is a total of 6 positive divisors.
The sum of these divisors is 1596.
The arithmetic mean is 266.

4 even divisors

2, 4, 454, 908

2 odd divisors

1, 227

How to compute the divisors of 908?

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 908 by each of the numbers from 1 to 908 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)

908 / 1 = 908 (the remainder is 0, so 1 is a divisor of 908)
908 / 2 = 454 (the remainder is 0, so 2 is a divisor of 908)
908 / 3 = 302.66666666667 (the remainder is 2, so 3 is not a divisor of 908)
...
908 / 907 = 1.0011025358324 (the remainder is 1, so 907 is not a divisor of 908)
908 / 908 = 1 (the remainder is 0, so 908 is a divisor of 908)

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 908 (i.e. 30.133038346639). 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 $\frac{N}{d} = D$ )

908 / 1 = 908 (the remainder is 0, so 1 and 908 are divisors of 908)
908 / 2 = 454 (the remainder is 0, so 2 and 454 are divisors of 908)
908 / 3 = 302.66666666667 (the remainder is 2, so 3 is not a divisor of 908)
...
908 / 29 = 31.310344827586 (the remainder is 9, so 29 is not a divisor of 908)
908 / 30 = 30.266666666667 (the remainder is 8, so 30 is not a divisor of 908)