What are the divisors of 957?

1, 3, 11, 29, 33, 87, 319, 957

There is a total of 8 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 180.

8 odd divisors

1, 3, 11, 29, 33, 87, 319, 957

How to compute the divisors of 957?

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 957 by each of the numbers from 1 to 957 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)

957 / 1 = 957 (the remainder is 0, so 1 is a divisor of 957)
957 / 2 = 478.5 (the remainder is 1, so 2 is not a divisor of 957)
957 / 3 = 319 (the remainder is 0, so 3 is a divisor of 957)
...
957 / 956 = 1.0010460251046 (the remainder is 1, so 956 is not a divisor of 957)
957 / 957 = 1 (the remainder is 0, so 957 is a divisor of 957)

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 957 (i.e. 30.935416596516). 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 $\frac{N}{d} = D$ )

957 / 1 = 957 (the remainder is 0, so 1 and 957 are divisors of 957)
957 / 2 = 478.5 (the remainder is 1, so 2 is not a divisor of 957)
957 / 3 = 319 (the remainder is 0, so 3 and 319 are divisors of 957)
...
957 / 29 = 33 (the remainder is 0, so 29 and 33 are divisors of 957)
957 / 30 = 31.9 (the remainder is 27, so 30 is not a divisor of 957)