What are the divisors of 1032?

1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032

There is a total of 16 positive divisors.
The sum of these divisors is 2640.
The arithmetic mean is 165.

12 even divisors

2, 4, 6, 8, 12, 24, 86, 172, 258, 344, 516, 1032

4 odd divisors

1, 3, 43, 129

How to compute the divisors of 1032?

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 1032 by each of the numbers from 1 to 1032 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)

1032 / 1 = 1032 (the remainder is 0, so 1 is a divisor of 1032)
1032 / 2 = 516 (the remainder is 0, so 2 is a divisor of 1032)
1032 / 3 = 344 (the remainder is 0, so 3 is a divisor of 1032)
...
1032 / 1031 = 1.0009699321048 (the remainder is 1, so 1031 is not a divisor of 1032)
1032 / 1032 = 1 (the remainder is 0, so 1032 is a divisor of 1032)

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 1032 (i.e. 32.124756808418). 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 $\frac{N}{d} = D$ )

1032 / 1 = 1032 (the remainder is 0, so 1 and 1032 are divisors of 1032)
1032 / 2 = 516 (the remainder is 0, so 2 and 516 are divisors of 1032)
1032 / 3 = 344 (the remainder is 0, so 3 and 344 are divisors of 1032)
...
1032 / 31 = 33.290322580645 (the remainder is 9, so 31 is not a divisor of 1032)
1032 / 32 = 32.25 (the remainder is 8, so 32 is not a divisor of 1032)