What are the divisors of 917?

1, 7, 131, 917

There is a total of 4 positive divisors.
The sum of these divisors is 1056.
The arithmetic mean is 264.

4 odd divisors

1, 7, 131, 917

How to compute the divisors of 917?

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 917 by each of the numbers from 1 to 917 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)

917 / 1 = 917 (the remainder is 0, so 1 is a divisor of 917)
917 / 2 = 458.5 (the remainder is 1, so 2 is not a divisor of 917)
917 / 3 = 305.66666666667 (the remainder is 2, so 3 is not a divisor of 917)
...
917 / 916 = 1.0010917030568 (the remainder is 1, so 916 is not a divisor of 917)
917 / 917 = 1 (the remainder is 0, so 917 is a divisor of 917)

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 917 (i.e. 30.282007859453). 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 $\frac{N}{d} = D$ )

917 / 1 = 917 (the remainder is 0, so 1 and 917 are divisors of 917)
917 / 2 = 458.5 (the remainder is 1, so 2 is not a divisor of 917)
917 / 3 = 305.66666666667 (the remainder is 2, so 3 is not a divisor of 917)
...
917 / 29 = 31.620689655172 (the remainder is 18, so 29 is not a divisor of 917)
917 / 30 = 30.566666666667 (the remainder is 17, so 30 is not a divisor of 917)