What are the divisors of 5538?

1, 2, 3, 6, 13, 26, 39, 71, 78, 142, 213, 426, 923, 1846, 2769, 5538

There is a total of 16 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 756.

8 even divisors

2, 6, 26, 78, 142, 426, 1846, 5538

8 odd divisors

1, 3, 13, 39, 71, 213, 923, 2769

How to compute the divisors of 5538?

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 5538 by each of the numbers from 1 to 5538 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)

5538 / 1 = 5538 (the remainder is 0, so 1 is a divisor of 5538)
5538 / 2 = 2769 (the remainder is 0, so 2 is a divisor of 5538)
5538 / 3 = 1846 (the remainder is 0, so 3 is a divisor of 5538)
...
5538 / 5537 = 1.0001806032147 (the remainder is 1, so 5537 is not a divisor of 5538)
5538 / 5538 = 1 (the remainder is 0, so 5538 is a divisor of 5538)

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 5538 (i.e. 74.417739820556). 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 $\frac{N}{d} = D$ )

5538 / 1 = 5538 (the remainder is 0, so 1 and 5538 are divisors of 5538)
5538 / 2 = 2769 (the remainder is 0, so 2 and 2769 are divisors of 5538)
5538 / 3 = 1846 (the remainder is 0, so 3 and 1846 are divisors of 5538)
...
5538 / 73 = 75.86301369863 (the remainder is 63, so 73 is not a divisor of 5538)
5538 / 74 = 74.837837837838 (the remainder is 62, so 74 is not a divisor of 5538)