What are the divisors of 5364?

1, 2, 3, 4, 6, 9, 12, 18, 36, 149, 298, 447, 596, 894, 1341, 1788, 2682, 5364

There is a total of 18 positive divisors.
The sum of these divisors is 13650.
The arithmetic mean is 758.33333333333.

12 even divisors

2, 4, 6, 12, 18, 36, 298, 596, 894, 1788, 2682, 5364

6 odd divisors

1, 3, 9, 149, 447, 1341

How to compute the divisors of 5364?

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 5364 by each of the numbers from 1 to 5364 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)

5364 / 1 = 5364 (the remainder is 0, so 1 is a divisor of 5364)
5364 / 2 = 2682 (the remainder is 0, so 2 is a divisor of 5364)
5364 / 3 = 1788 (the remainder is 0, so 3 is a divisor of 5364)
...
5364 / 5363 = 1.0001864628007 (the remainder is 1, so 5363 is not a divisor of 5364)
5364 / 5364 = 1 (the remainder is 0, so 5364 is a divisor of 5364)

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 5364 (i.e. 73.239333694402). 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 $\frac{N}{d} = D$ )

5364 / 1 = 5364 (the remainder is 0, so 1 and 5364 are divisors of 5364)
5364 / 2 = 2682 (the remainder is 0, so 2 and 2682 are divisors of 5364)
5364 / 3 = 1788 (the remainder is 0, so 3 and 1788 are divisors of 5364)
...
5364 / 72 = 74.5 (the remainder is 36, so 72 is not a divisor of 5364)
5364 / 73 = 73.479452054795 (the remainder is 35, so 73 is not a divisor of 5364)