What are the divisors of 316?

1, 2, 4, 79, 158, 316

There is a total of 6 positive divisors.
The sum of these divisors is 560.
The arithmetic mean is 93.333333333333.

4 even divisors

2, 4, 158, 316

2 odd divisors

1, 79

How to compute the divisors of 316?

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 316 by each of the numbers from 1 to 316 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)

316 / 1 = 316 (the remainder is 0, so 1 is a divisor of 316)
316 / 2 = 158 (the remainder is 0, so 2 is a divisor of 316)
316 / 3 = 105.33333333333 (the remainder is 1, so 3 is not a divisor of 316)
...
316 / 315 = 1.0031746031746 (the remainder is 1, so 315 is not a divisor of 316)
316 / 316 = 1 (the remainder is 0, so 316 is a divisor of 316)

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 316 (i.e. 17.776388834631). 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 $\frac{N}{d} = D$ )

316 / 1 = 316 (the remainder is 0, so 1 and 316 are divisors of 316)
316 / 2 = 158 (the remainder is 0, so 2 and 158 are divisors of 316)
316 / 3 = 105.33333333333 (the remainder is 1, so 3 is not a divisor of 316)
...
316 / 16 = 19.75 (the remainder is 12, so 16 is not a divisor of 316)
316 / 17 = 18.588235294118 (the remainder is 10, so 17 is not a divisor of 316)