What are the divisors of 5388?

1, 2, 3, 4, 6, 12, 449, 898, 1347, 1796, 2694, 5388

There is a total of 12 positive divisors.
The sum of these divisors is 12600.
The arithmetic mean is 1050.

8 even divisors

2, 4, 6, 12, 898, 1796, 2694, 5388

4 odd divisors

1, 3, 449, 1347

How to compute the divisors of 5388?

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 5388 by each of the numbers from 1 to 5388 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)

5388 / 1 = 5388 (the remainder is 0, so 1 is a divisor of 5388)
5388 / 2 = 2694 (the remainder is 0, so 2 is a divisor of 5388)
5388 / 3 = 1796 (the remainder is 0, so 3 is a divisor of 5388)
...
5388 / 5387 = 1.0001856320772 (the remainder is 1, so 5387 is not a divisor of 5388)
5388 / 5388 = 1 (the remainder is 0, so 5388 is a divisor of 5388)

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 5388 (i.e. 73.40299721401). 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 $\frac{N}{d} = D$ )

5388 / 1 = 5388 (the remainder is 0, so 1 and 5388 are divisors of 5388)
5388 / 2 = 2694 (the remainder is 0, so 2 and 2694 are divisors of 5388)
5388 / 3 = 1796 (the remainder is 0, so 3 and 1796 are divisors of 5388)
...
5388 / 72 = 74.833333333333 (the remainder is 60, so 72 is not a divisor of 5388)
5388 / 73 = 73.808219178082 (the remainder is 59, so 73 is not a divisor of 5388)