What are the divisors of 5484?

1, 2, 3, 4, 6, 12, 457, 914, 1371, 1828, 2742, 5484

There is a total of 12 positive divisors.
The sum of these divisors is 12824.
The arithmetic mean is 1068.6666666667.

8 even divisors

2, 4, 6, 12, 914, 1828, 2742, 5484

4 odd divisors

1, 3, 457, 1371

How to compute the divisors of 5484?

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 5484 by each of the numbers from 1 to 5484 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)

5484 / 1 = 5484 (the remainder is 0, so 1 is a divisor of 5484)
5484 / 2 = 2742 (the remainder is 0, so 2 is a divisor of 5484)
5484 / 3 = 1828 (the remainder is 0, so 3 is a divisor of 5484)
...
5484 / 5483 = 1.0001823819077 (the remainder is 1, so 5483 is not a divisor of 5484)
5484 / 5484 = 1 (the remainder is 0, so 5484 is a divisor of 5484)

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 5484 (i.e. 74.054034326294). 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 $\frac{N}{d} = D$ )

5484 / 1 = 5484 (the remainder is 0, so 1 and 5484 are divisors of 5484)
5484 / 2 = 2742 (the remainder is 0, so 2 and 2742 are divisors of 5484)
5484 / 3 = 1828 (the remainder is 0, so 3 and 1828 are divisors of 5484)
...
5484 / 73 = 75.123287671233 (the remainder is 9, so 73 is not a divisor of 5484)
5484 / 74 = 74.108108108108 (the remainder is 8, so 74 is not a divisor of 5484)