What are the divisors of 979?

1, 11, 89, 979

There is a total of 4 positive divisors.
The sum of these divisors is 1080.
The arithmetic mean is 270.

4 odd divisors

1, 11, 89, 979

How to compute the divisors of 979?

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 979 by each of the numbers from 1 to 979 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)

979 / 1 = 979 (the remainder is 0, so 1 is a divisor of 979)
979 / 2 = 489.5 (the remainder is 1, so 2 is not a divisor of 979)
979 / 3 = 326.33333333333 (the remainder is 1, so 3 is not a divisor of 979)
...
979 / 978 = 1.0010224948875 (the remainder is 1, so 978 is not a divisor of 979)
979 / 979 = 1 (the remainder is 0, so 979 is a divisor of 979)

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 979 (i.e. 31.288975694324). 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 $\frac{N}{d} = D$ )

979 / 1 = 979 (the remainder is 0, so 1 and 979 are divisors of 979)
979 / 2 = 489.5 (the remainder is 1, so 2 is not a divisor of 979)
979 / 3 = 326.33333333333 (the remainder is 1, so 3 is not a divisor of 979)
...
979 / 30 = 32.633333333333 (the remainder is 19, so 30 is not a divisor of 979)
979 / 31 = 31.58064516129 (the remainder is 18, so 31 is not a divisor of 979)