What are the divisors of 432?

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 216, 432

There is a total of 20 positive divisors.
The sum of these divisors is 1240.
The arithmetic mean is 62.

16 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 36, 48, 54, 72, 108, 144, 216, 432

4 odd divisors

1, 3, 9, 27

How to compute the divisors of 432?

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 432 by each of the numbers from 1 to 432 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)

432 / 1 = 432 (the remainder is 0, so 1 is a divisor of 432)
432 / 2 = 216 (the remainder is 0, so 2 is a divisor of 432)
432 / 3 = 144 (the remainder is 0, so 3 is a divisor of 432)
...
432 / 431 = 1.0023201856148 (the remainder is 1, so 431 is not a divisor of 432)
432 / 432 = 1 (the remainder is 0, so 432 is a divisor of 432)

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 432 (i.e. 20.784609690827). 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 $\frac{N}{d} = D$ )

432 / 1 = 432 (the remainder is 0, so 1 and 432 are divisors of 432)
432 / 2 = 216 (the remainder is 0, so 2 and 216 are divisors of 432)
432 / 3 = 144 (the remainder is 0, so 3 and 144 are divisors of 432)
...
432 / 19 = 22.736842105263 (the remainder is 14, so 19 is not a divisor of 432)
432 / 20 = 21.6 (the remainder is 12, so 20 is not a divisor of 432)