What are the divisors of 951?

1, 3, 317, 951

There is a total of 4 positive divisors.
The sum of these divisors is 1272.
The arithmetic mean is 318.

4 odd divisors

1, 3, 317, 951

How to compute the divisors of 951?

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 951 by each of the numbers from 1 to 951 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)

951 / 1 = 951 (the remainder is 0, so 1 is a divisor of 951)
951 / 2 = 475.5 (the remainder is 1, so 2 is not a divisor of 951)
951 / 3 = 317 (the remainder is 0, so 3 is a divisor of 951)
...
951 / 950 = 1.0010526315789 (the remainder is 1, so 950 is not a divisor of 951)
951 / 951 = 1 (the remainder is 0, so 951 is a divisor of 951)

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 951 (i.e. 30.838287890219). 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 $\frac{N}{d} = D$ )

951 / 1 = 951 (the remainder is 0, so 1 and 951 are divisors of 951)
951 / 2 = 475.5 (the remainder is 1, so 2 is not a divisor of 951)
951 / 3 = 317 (the remainder is 0, so 3 and 317 are divisors of 951)
...
951 / 29 = 32.793103448276 (the remainder is 23, so 29 is not a divisor of 951)
951 / 30 = 31.7 (the remainder is 21, so 30 is not a divisor of 951)