What are the divisors of 5448?

1, 2, 3, 4, 6, 8, 12, 24, 227, 454, 681, 908, 1362, 1816, 2724, 5448

There is a total of 16 positive divisors.
The sum of these divisors is 13680.
The arithmetic mean is 855.

12 even divisors

2, 4, 6, 8, 12, 24, 454, 908, 1362, 1816, 2724, 5448

4 odd divisors

1, 3, 227, 681

How to compute the divisors of 5448?

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 5448 by each of the numbers from 1 to 5448 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)

5448 / 1 = 5448 (the remainder is 0, so 1 is a divisor of 5448)
5448 / 2 = 2724 (the remainder is 0, so 2 is a divisor of 5448)
5448 / 3 = 1816 (the remainder is 0, so 3 is a divisor of 5448)
...
5448 / 5447 = 1.0001835872958 (the remainder is 1, so 5447 is not a divisor of 5448)
5448 / 5448 = 1 (the remainder is 0, so 5448 is a divisor of 5448)

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 5448 (i.e. 73.810568348984). 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 $\frac{N}{d} = D$ )

5448 / 1 = 5448 (the remainder is 0, so 1 and 5448 are divisors of 5448)
5448 / 2 = 2724 (the remainder is 0, so 2 and 2724 are divisors of 5448)
5448 / 3 = 1816 (the remainder is 0, so 3 and 1816 are divisors of 5448)
...
5448 / 72 = 75.666666666667 (the remainder is 48, so 72 is not a divisor of 5448)
5448 / 73 = 74.630136986301 (the remainder is 46, so 73 is not a divisor of 5448)