What are the divisors of 915?

1, 3, 5, 15, 61, 183, 305, 915

There is a total of 8 positive divisors.
The sum of these divisors is 1488.
The arithmetic mean is 186.

8 odd divisors

1, 3, 5, 15, 61, 183, 305, 915

How to compute the divisors of 915?

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 915 by each of the numbers from 1 to 915 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)

915 / 1 = 915 (the remainder is 0, so 1 is a divisor of 915)
915 / 2 = 457.5 (the remainder is 1, so 2 is not a divisor of 915)
915 / 3 = 305 (the remainder is 0, so 3 is a divisor of 915)
...
915 / 914 = 1.0010940919037 (the remainder is 1, so 914 is not a divisor of 915)
915 / 915 = 1 (the remainder is 0, so 915 is a divisor of 915)

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 915 (i.e. 30.248966924508). 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 $\frac{N}{d} = D$ )

915 / 1 = 915 (the remainder is 0, so 1 and 915 are divisors of 915)
915 / 2 = 457.5 (the remainder is 1, so 2 is not a divisor of 915)
915 / 3 = 305 (the remainder is 0, so 3 and 305 are divisors of 915)
...
915 / 29 = 31.551724137931 (the remainder is 16, so 29 is not a divisor of 915)
915 / 30 = 30.5 (the remainder is 15, so 30 is not a divisor of 915)