What are the divisors of 953?

1, 953

There is a total of 2 positive divisors.
The sum of these divisors is 954.
The arithmetic mean is 477.

2 odd divisors

1, 953

How to compute the divisors of 953?

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 953 by each of the numbers from 1 to 953 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)

953 / 1 = 953 (the remainder is 0, so 1 is a divisor of 953)
953 / 2 = 476.5 (the remainder is 1, so 2 is not a divisor of 953)
953 / 3 = 317.66666666667 (the remainder is 2, so 3 is not a divisor of 953)
...
953 / 952 = 1.0010504201681 (the remainder is 1, so 952 is not a divisor of 953)
953 / 953 = 1 (the remainder is 0, so 953 is a divisor of 953)

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 953 (i.e. 30.870698080866). 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 $\frac{N}{d} = D$ )

953 / 1 = 953 (the remainder is 0, so 1 and 953 are divisors of 953)
953 / 2 = 476.5 (the remainder is 1, so 2 is not a divisor of 953)
953 / 3 = 317.66666666667 (the remainder is 2, so 3 is not a divisor of 953)
...
953 / 29 = 32.862068965517 (the remainder is 25, so 29 is not a divisor of 953)
953 / 30 = 31.766666666667 (the remainder is 23, so 30 is not a divisor of 953)