What are the divisors of 952?

1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952

There is a total of 16 positive divisors.
The sum of these divisors is 2160.
The arithmetic mean is 135.

12 even divisors

2, 4, 8, 14, 28, 34, 56, 68, 136, 238, 476, 952

4 odd divisors

1, 7, 17, 119

How to compute the divisors of 952?

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 952 by each of the numbers from 1 to 952 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)

952 / 1 = 952 (the remainder is 0, so 1 is a divisor of 952)
952 / 2 = 476 (the remainder is 0, so 2 is a divisor of 952)
952 / 3 = 317.33333333333 (the remainder is 1, so 3 is not a divisor of 952)
...
952 / 951 = 1.0010515247108 (the remainder is 1, so 951 is not a divisor of 952)
952 / 952 = 1 (the remainder is 0, so 952 is a divisor of 952)

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 952 (i.e. 30.854497241083). 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 $\frac{N}{d} = D$ )

952 / 1 = 952 (the remainder is 0, so 1 and 952 are divisors of 952)
952 / 2 = 476 (the remainder is 0, so 2 and 476 are divisors of 952)
952 / 3 = 317.33333333333 (the remainder is 1, so 3 is not a divisor of 952)
...
952 / 29 = 32.827586206897 (the remainder is 24, so 29 is not a divisor of 952)
952 / 30 = 31.733333333333 (the remainder is 22, so 30 is not a divisor of 952)