What are the divisors of 3288?

1, 2, 3, 4, 6, 8, 12, 24, 137, 274, 411, 548, 822, 1096, 1644, 3288

There is a total of 16 positive divisors.
The sum of these divisors is 8280.
The arithmetic mean is 517.5.

12 even divisors

2, 4, 6, 8, 12, 24, 274, 548, 822, 1096, 1644, 3288

4 odd divisors

1, 3, 137, 411

How to compute the divisors of 3288?

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 3288 by each of the numbers from 1 to 3288 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)

3288 / 1 = 3288 (the remainder is 0, so 1 is a divisor of 3288)
3288 / 2 = 1644 (the remainder is 0, so 2 is a divisor of 3288)
3288 / 3 = 1096 (the remainder is 0, so 3 is a divisor of 3288)
...
3288 / 3287 = 1.00030422878 (the remainder is 1, so 3287 is not a divisor of 3288)
3288 / 3288 = 1 (the remainder is 0, so 3288 is a divisor of 3288)

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 3288 (i.e. 57.341084747326). 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 $\frac{N}{d} = D$ )

3288 / 1 = 3288 (the remainder is 0, so 1 and 3288 are divisors of 3288)
3288 / 2 = 1644 (the remainder is 0, so 2 and 1644 are divisors of 3288)
3288 / 3 = 1096 (the remainder is 0, so 3 and 1096 are divisors of 3288)
...
3288 / 56 = 58.714285714286 (the remainder is 40, so 56 is not a divisor of 3288)
3288 / 57 = 57.684210526316 (the remainder is 39, so 57 is not a divisor of 3288)