What are the divisors of 959?

1, 7, 137, 959

There is a total of 4 positive divisors.
The sum of these divisors is 1104.
The arithmetic mean is 276.

4 odd divisors

1, 7, 137, 959

How to compute the divisors of 959?

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 959 by each of the numbers from 1 to 959 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)

959 / 1 = 959 (the remainder is 0, so 1 is a divisor of 959)
959 / 2 = 479.5 (the remainder is 1, so 2 is not a divisor of 959)
959 / 3 = 319.66666666667 (the remainder is 2, so 3 is not a divisor of 959)
...
959 / 958 = 1.0010438413361 (the remainder is 1, so 958 is not a divisor of 959)
959 / 959 = 1 (the remainder is 0, so 959 is a divisor of 959)

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 959 (i.e. 30.967725134404). 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 $\frac{N}{d} = D$ )

959 / 1 = 959 (the remainder is 0, so 1 and 959 are divisors of 959)
959 / 2 = 479.5 (the remainder is 1, so 2 is not a divisor of 959)
959 / 3 = 319.66666666667 (the remainder is 2, so 3 is not a divisor of 959)
...
959 / 29 = 33.068965517241 (the remainder is 2, so 29 is not a divisor of 959)
959 / 30 = 31.966666666667 (the remainder is 29, so 30 is not a divisor of 959)