What are the divisors of 3432?

1, 2, 3, 4, 6, 8, 11, 12, 13, 22, 24, 26, 33, 39, 44, 52, 66, 78, 88, 104, 132, 143, 156, 264, 286, 312, 429, 572, 858, 1144, 1716, 3432

There is a total of 32 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 315.

24 even divisors

2, 4, 6, 8, 12, 22, 24, 26, 44, 52, 66, 78, 88, 104, 132, 156, 264, 286, 312, 572, 858, 1144, 1716, 3432

8 odd divisors

1, 3, 11, 13, 33, 39, 143, 429

How to compute the divisors of 3432?

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 3432 by each of the numbers from 1 to 3432 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)

3432 / 1 = 3432 (the remainder is 0, so 1 is a divisor of 3432)
3432 / 2 = 1716 (the remainder is 0, so 2 is a divisor of 3432)
3432 / 3 = 1144 (the remainder is 0, so 3 is a divisor of 3432)
...
3432 / 3431 = 1.0002914602157 (the remainder is 1, so 3431 is not a divisor of 3432)
3432 / 3432 = 1 (the remainder is 0, so 3432 is a divisor of 3432)

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 3432 (i.e. 58.583274063507). 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 $\frac{N}{d} = D$ )

3432 / 1 = 3432 (the remainder is 0, so 1 and 3432 are divisors of 3432)
3432 / 2 = 1716 (the remainder is 0, so 2 and 1716 are divisors of 3432)
3432 / 3 = 1144 (the remainder is 0, so 3 and 1144 are divisors of 3432)
...
3432 / 57 = 60.210526315789 (the remainder is 12, so 57 is not a divisor of 3432)
3432 / 58 = 59.172413793103 (the remainder is 10, so 58 is not a divisor of 3432)