What are the divisors of 1632?

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 68, 96, 102, 136, 204, 272, 408, 544, 816, 1632

There is a total of 24 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 189.

20 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 34, 48, 68, 96, 102, 136, 204, 272, 408, 544, 816, 1632

4 odd divisors

1, 3, 17, 51

How to compute the divisors of 1632?

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 1632 by each of the numbers from 1 to 1632 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)

1632 / 1 = 1632 (the remainder is 0, so 1 is a divisor of 1632)
1632 / 2 = 816 (the remainder is 0, so 2 is a divisor of 1632)
1632 / 3 = 544 (the remainder is 0, so 3 is a divisor of 1632)
...
1632 / 1631 = 1.0006131207848 (the remainder is 1, so 1631 is not a divisor of 1632)
1632 / 1632 = 1 (the remainder is 0, so 1632 is a divisor of 1632)

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 1632 (i.e. 40.398019753448). 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 $\frac{N}{d} = D$ )

1632 / 1 = 1632 (the remainder is 0, so 1 and 1632 are divisors of 1632)
1632 / 2 = 816 (the remainder is 0, so 2 and 816 are divisors of 1632)
1632 / 3 = 544 (the remainder is 0, so 3 and 544 are divisors of 1632)
...
1632 / 39 = 41.846153846154 (the remainder is 33, so 39 is not a divisor of 1632)
1632 / 40 = 40.8 (the remainder is 32, so 40 is not a divisor of 1632)