What are the divisors of 5328?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 37, 48, 72, 74, 111, 144, 148, 222, 296, 333, 444, 592, 666, 888, 1332, 1776, 2664, 5328

There is a total of 30 positive divisors.
The sum of these divisors is 15314.
The arithmetic mean is 510.46666666667.

24 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 74, 144, 148, 222, 296, 444, 592, 666, 888, 1332, 1776, 2664, 5328

6 odd divisors

1, 3, 9, 37, 111, 333

How to compute the divisors of 5328?

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 5328 by each of the numbers from 1 to 5328 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)

5328 / 1 = 5328 (the remainder is 0, so 1 is a divisor of 5328)
5328 / 2 = 2664 (the remainder is 0, so 2 is a divisor of 5328)
5328 / 3 = 1776 (the remainder is 0, so 3 is a divisor of 5328)
...
5328 / 5327 = 1.000187722921 (the remainder is 1, so 5327 is not a divisor of 5328)
5328 / 5328 = 1 (the remainder is 0, so 5328 is a divisor of 5328)

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 5328 (i.e. 72.993150363579). 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 $\frac{N}{d} = D$ )

5328 / 1 = 5328 (the remainder is 0, so 1 and 5328 are divisors of 5328)
5328 / 2 = 2664 (the remainder is 0, so 2 and 2664 are divisors of 5328)
5328 / 3 = 1776 (the remainder is 0, so 3 and 1776 are divisors of 5328)
...
5328 / 71 = 75.042253521127 (the remainder is 3, so 71 is not a divisor of 5328)
5328 / 72 = 74 (the remainder is 0, so 72 and 74 are divisors of 5328)