What are the divisors of 5424?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 113, 226, 339, 452, 678, 904, 1356, 1808, 2712, 5424

There is a total of 20 positive divisors.
The sum of these divisors is 14136.
The arithmetic mean is 706.8.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 226, 452, 678, 904, 1356, 1808, 2712, 5424

4 odd divisors

1, 3, 113, 339

How to compute the divisors of 5424?

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 5424 by each of the numbers from 1 to 5424 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)

5424 / 1 = 5424 (the remainder is 0, so 1 is a divisor of 5424)
5424 / 2 = 2712 (the remainder is 0, so 2 is a divisor of 5424)
5424 / 3 = 1808 (the remainder is 0, so 3 is a divisor of 5424)
...
5424 / 5423 = 1.0001843997787 (the remainder is 1, so 5423 is not a divisor of 5424)
5424 / 5424 = 1 (the remainder is 0, so 5424 is a divisor of 5424)

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 5424 (i.e. 73.647810558088). 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 $\frac{N}{d} = D$ )

5424 / 1 = 5424 (the remainder is 0, so 1 and 5424 are divisors of 5424)
5424 / 2 = 2712 (the remainder is 0, so 2 and 2712 are divisors of 5424)
5424 / 3 = 1808 (the remainder is 0, so 3 and 1808 are divisors of 5424)
...
5424 / 72 = 75.333333333333 (the remainder is 24, so 72 is not a divisor of 5424)
5424 / 73 = 74.301369863014 (the remainder is 22, so 73 is not a divisor of 5424)