What are the divisors of 913?

1, 11, 83, 913

There is a total of 4 positive divisors.
The sum of these divisors is 1008.
The arithmetic mean is 252.

4 odd divisors

1, 11, 83, 913

How to compute the divisors of 913?

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 913 by each of the numbers from 1 to 913 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)

913 / 1 = 913 (the remainder is 0, so 1 is a divisor of 913)
913 / 2 = 456.5 (the remainder is 1, so 2 is not a divisor of 913)
913 / 3 = 304.33333333333 (the remainder is 1, so 3 is not a divisor of 913)
...
913 / 912 = 1.0010964912281 (the remainder is 1, so 912 is not a divisor of 913)
913 / 913 = 1 (the remainder is 0, so 913 is a divisor of 913)

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 913 (i.e. 30.215889859476). 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 $\frac{N}{d} = D$ )

913 / 1 = 913 (the remainder is 0, so 1 and 913 are divisors of 913)
913 / 2 = 456.5 (the remainder is 1, so 2 is not a divisor of 913)
913 / 3 = 304.33333333333 (the remainder is 1, so 3 is not a divisor of 913)
...
913 / 29 = 31.48275862069 (the remainder is 14, so 29 is not a divisor of 913)
913 / 30 = 30.433333333333 (the remainder is 13, so 30 is not a divisor of 913)