What are the divisors of 955?

1, 5, 191, 955

There is a total of 4 positive divisors.
The sum of these divisors is 1152.
The arithmetic mean is 288.

4 odd divisors

1, 5, 191, 955

How to compute the divisors of 955?

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 955 by each of the numbers from 1 to 955 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)

955 / 1 = 955 (the remainder is 0, so 1 is a divisor of 955)
955 / 2 = 477.5 (the remainder is 1, so 2 is not a divisor of 955)
955 / 3 = 318.33333333333 (the remainder is 1, so 3 is not a divisor of 955)
...
955 / 954 = 1.0010482180294 (the remainder is 1, so 954 is not a divisor of 955)
955 / 955 = 1 (the remainder is 0, so 955 is a divisor of 955)

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 955 (i.e. 30.903074280725). 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 $\frac{N}{d} = D$ )

955 / 1 = 955 (the remainder is 0, so 1 and 955 are divisors of 955)
955 / 2 = 477.5 (the remainder is 1, so 2 is not a divisor of 955)
955 / 3 = 318.33333333333 (the remainder is 1, so 3 is not a divisor of 955)
...
955 / 29 = 32.931034482759 (the remainder is 27, so 29 is not a divisor of 955)
955 / 30 = 31.833333333333 (the remainder is 25, so 30 is not a divisor of 955)