What are the divisors of 916?

1, 2, 4, 229, 458, 916

There is a total of 6 positive divisors.
The sum of these divisors is 1610.
The arithmetic mean is 268.33333333333.

4 even divisors

2, 4, 458, 916

2 odd divisors

1, 229

How to compute the divisors of 916?

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 916 by each of the numbers from 1 to 916 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)

916 / 1 = 916 (the remainder is 0, so 1 is a divisor of 916)
916 / 2 = 458 (the remainder is 0, so 2 is a divisor of 916)
916 / 3 = 305.33333333333 (the remainder is 1, so 3 is not a divisor of 916)
...
916 / 915 = 1.0010928961749 (the remainder is 1, so 915 is not a divisor of 916)
916 / 916 = 1 (the remainder is 0, so 916 is a divisor of 916)

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 916 (i.e. 30.265491900843). 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 $\frac{N}{d} = D$ )

916 / 1 = 916 (the remainder is 0, so 1 and 916 are divisors of 916)
916 / 2 = 458 (the remainder is 0, so 2 and 458 are divisors of 916)
916 / 3 = 305.33333333333 (the remainder is 1, so 3 is not a divisor of 916)
...
916 / 29 = 31.586206896552 (the remainder is 17, so 29 is not a divisor of 916)
916 / 30 = 30.533333333333 (the remainder is 16, so 30 is not a divisor of 916)