What are the divisors of 968?

1, 2, 4, 8, 11, 22, 44, 88, 121, 242, 484, 968

There is a total of 12 positive divisors.
The sum of these divisors is 1995.
The arithmetic mean is 166.25.

9 even divisors

2, 4, 8, 22, 44, 88, 242, 484, 968

3 odd divisors

1, 11, 121

How to compute the divisors of 968?

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 968 by each of the numbers from 1 to 968 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)

968 / 1 = 968 (the remainder is 0, so 1 is a divisor of 968)
968 / 2 = 484 (the remainder is 0, so 2 is a divisor of 968)
968 / 3 = 322.66666666667 (the remainder is 2, so 3 is not a divisor of 968)
...
968 / 967 = 1.0010341261634 (the remainder is 1, so 967 is not a divisor of 968)
968 / 968 = 1 (the remainder is 0, so 968 is a divisor of 968)

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 968 (i.e. 31.112698372208). 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 $\frac{N}{d} = D$ )

968 / 1 = 968 (the remainder is 0, so 1 and 968 are divisors of 968)
968 / 2 = 484 (the remainder is 0, so 2 and 484 are divisors of 968)
968 / 3 = 322.66666666667 (the remainder is 2, so 3 is not a divisor of 968)
...
968 / 30 = 32.266666666667 (the remainder is 8, so 30 is not a divisor of 968)
968 / 31 = 31.225806451613 (the remainder is 7, so 31 is not a divisor of 968)