What are the divisors of 5430?

1, 2, 3, 5, 6, 10, 15, 30, 181, 362, 543, 905, 1086, 1810, 2715, 5430

There is a total of 16 positive divisors.
The sum of these divisors is 13104.
The arithmetic mean is 819.

8 even divisors

2, 6, 10, 30, 362, 1086, 1810, 5430

8 odd divisors

1, 3, 5, 15, 181, 543, 905, 2715

How to compute the divisors of 5430?

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 5430 by each of the numbers from 1 to 5430 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)

5430 / 1 = 5430 (the remainder is 0, so 1 is a divisor of 5430)
5430 / 2 = 2715 (the remainder is 0, so 2 is a divisor of 5430)
5430 / 3 = 1810 (the remainder is 0, so 3 is a divisor of 5430)
...
5430 / 5429 = 1.0001841959845 (the remainder is 1, so 5429 is not a divisor of 5430)
5430 / 5430 = 1 (the remainder is 0, so 5430 is a divisor of 5430)

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 5430 (i.e. 73.688533707762). 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 $\frac{N}{d} = D$ )

5430 / 1 = 5430 (the remainder is 0, so 1 and 5430 are divisors of 5430)
5430 / 2 = 2715 (the remainder is 0, so 2 and 2715 are divisors of 5430)
5430 / 3 = 1810 (the remainder is 0, so 3 and 1810 are divisors of 5430)
...
5430 / 72 = 75.416666666667 (the remainder is 30, so 72 is not a divisor of 5430)
5430 / 73 = 74.383561643836 (the remainder is 28, so 73 is not a divisor of 5430)