What are the divisors of 956?

1, 2, 4, 239, 478, 956

There is a total of 6 positive divisors.
The sum of these divisors is 1680.
The arithmetic mean is 280.

4 even divisors

2, 4, 478, 956

2 odd divisors

1, 239

How to compute the divisors of 956?

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 956 by each of the numbers from 1 to 956 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)

956 / 1 = 956 (the remainder is 0, so 1 is a divisor of 956)
956 / 2 = 478 (the remainder is 0, so 2 is a divisor of 956)
956 / 3 = 318.66666666667 (the remainder is 2, so 3 is not a divisor of 956)
...
956 / 955 = 1.0010471204188 (the remainder is 1, so 955 is not a divisor of 956)
956 / 956 = 1 (the remainder is 0, so 956 is a divisor of 956)

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 956 (i.e. 30.919249667481). 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 $\frac{N}{d} = D$ )

956 / 1 = 956 (the remainder is 0, so 1 and 956 are divisors of 956)
956 / 2 = 478 (the remainder is 0, so 2 and 478 are divisors of 956)
956 / 3 = 318.66666666667 (the remainder is 2, so 3 is not a divisor of 956)
...
956 / 29 = 32.965517241379 (the remainder is 28, so 29 is not a divisor of 956)
956 / 30 = 31.866666666667 (the remainder is 26, so 30 is not a divisor of 956)