What are the divisors of 5316?

1, 2, 3, 4, 6, 12, 443, 886, 1329, 1772, 2658, 5316

There is a total of 12 positive divisors.
The sum of these divisors is 12432.
The arithmetic mean is 1036.

8 even divisors

2, 4, 6, 12, 886, 1772, 2658, 5316

4 odd divisors

1, 3, 443, 1329

How to compute the divisors of 5316?

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 5316 by each of the numbers from 1 to 5316 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)

5316 / 1 = 5316 (the remainder is 0, so 1 is a divisor of 5316)
5316 / 2 = 2658 (the remainder is 0, so 2 is a divisor of 5316)
5316 / 3 = 1772 (the remainder is 0, so 3 is a divisor of 5316)
...
5316 / 5315 = 1.0001881467545 (the remainder is 1, so 5315 is not a divisor of 5316)
5316 / 5316 = 1 (the remainder is 0, so 5316 is a divisor of 5316)

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 5316 (i.e. 72.910904534233). 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 $\frac{N}{d} = D$ )

5316 / 1 = 5316 (the remainder is 0, so 1 and 5316 are divisors of 5316)
5316 / 2 = 2658 (the remainder is 0, so 2 and 2658 are divisors of 5316)
5316 / 3 = 1772 (the remainder is 0, so 3 and 1772 are divisors of 5316)
...
5316 / 71 = 74.87323943662 (the remainder is 62, so 71 is not a divisor of 5316)
5316 / 72 = 73.833333333333 (the remainder is 60, so 72 is not a divisor of 5316)