What are the divisors of 918?

1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 102, 153, 306, 459, 918

There is a total of 16 positive divisors.
The sum of these divisors is 2160.
The arithmetic mean is 135.

8 even divisors

2, 6, 18, 34, 54, 102, 306, 918

8 odd divisors

1, 3, 9, 17, 27, 51, 153, 459

How to compute the divisors of 918?

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 918 by each of the numbers from 1 to 918 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)

918 / 1 = 918 (the remainder is 0, so 1 is a divisor of 918)
918 / 2 = 459 (the remainder is 0, so 2 is a divisor of 918)
918 / 3 = 306 (the remainder is 0, so 3 is a divisor of 918)
...
918 / 917 = 1.0010905125409 (the remainder is 1, so 917 is not a divisor of 918)
918 / 918 = 1 (the remainder is 0, so 918 is a divisor of 918)

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 918 (i.e. 30.298514815086). 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 $\frac{N}{d} = D$ )

918 / 1 = 918 (the remainder is 0, so 1 and 918 are divisors of 918)
918 / 2 = 459 (the remainder is 0, so 2 and 459 are divisors of 918)
918 / 3 = 306 (the remainder is 0, so 3 and 306 are divisors of 918)
...
918 / 29 = 31.655172413793 (the remainder is 19, so 29 is not a divisor of 918)
918 / 30 = 30.6 (the remainder is 18, so 30 is not a divisor of 918)