What are the divisors of 958?

1, 2, 479, 958

There is a total of 4 positive divisors.
The sum of these divisors is 1440.
The arithmetic mean is 360.

2 even divisors

2, 958

2 odd divisors

1, 479

How to compute the divisors of 958?

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 958 by each of the numbers from 1 to 958 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)

958 / 1 = 958 (the remainder is 0, so 1 is a divisor of 958)
958 / 2 = 479 (the remainder is 0, so 2 is a divisor of 958)
958 / 3 = 319.33333333333 (the remainder is 1, so 3 is not a divisor of 958)
...
958 / 957 = 1.0010449320794 (the remainder is 1, so 957 is not a divisor of 958)
958 / 958 = 1 (the remainder is 0, so 958 is a divisor of 958)

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 958 (i.e. 30.951575081084). 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 $\frac{N}{d} = D$ )

958 / 1 = 958 (the remainder is 0, so 1 and 958 are divisors of 958)
958 / 2 = 479 (the remainder is 0, so 2 and 479 are divisors of 958)
958 / 3 = 319.33333333333 (the remainder is 1, so 3 is not a divisor of 958)
...
958 / 29 = 33.034482758621 (the remainder is 1, so 29 is not a divisor of 958)
958 / 30 = 31.933333333333 (the remainder is 28, so 30 is not a divisor of 958)