What are the divisors of 3264?

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 32, 34, 48, 51, 64, 68, 96, 102, 136, 192, 204, 272, 408, 544, 816, 1088, 1632, 3264

There is a total of 28 positive divisors.
The sum of these divisors is 9144.
The arithmetic mean is 326.57142857143.

24 even divisors

2, 4, 6, 8, 12, 16, 24, 32, 34, 48, 64, 68, 96, 102, 136, 192, 204, 272, 408, 544, 816, 1088, 1632, 3264

4 odd divisors

1, 3, 17, 51

How to compute the divisors of 3264?

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 3264 by each of the numbers from 1 to 3264 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)

3264 / 1 = 3264 (the remainder is 0, so 1 is a divisor of 3264)
3264 / 2 = 1632 (the remainder is 0, so 2 is a divisor of 3264)
3264 / 3 = 1088 (the remainder is 0, so 3 is a divisor of 3264)
...
3264 / 3263 = 1.0003064664419 (the remainder is 1, so 3263 is not a divisor of 3264)
3264 / 3264 = 1 (the remainder is 0, so 3264 is a divisor of 3264)

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 3264 (i.e. 57.131427428343). 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 $\frac{N}{d} = D$ )

3264 / 1 = 3264 (the remainder is 0, so 1 and 3264 are divisors of 3264)
3264 / 2 = 1632 (the remainder is 0, so 2 and 1632 are divisors of 3264)
3264 / 3 = 1088 (the remainder is 0, so 3 and 1088 are divisors of 3264)
...
3264 / 56 = 58.285714285714 (the remainder is 16, so 56 is not a divisor of 3264)
3264 / 57 = 57.263157894737 (the remainder is 15, so 57 is not a divisor of 3264)