What are the divisors of 3252?

1, 2, 3, 4, 6, 12, 271, 542, 813, 1084, 1626, 3252

There is a total of 12 positive divisors.
The sum of these divisors is 7616.
The arithmetic mean is 634.66666666667.

8 even divisors

2, 4, 6, 12, 542, 1084, 1626, 3252

4 odd divisors

1, 3, 271, 813

How to compute the divisors of 3252?

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 3252 by each of the numbers from 1 to 3252 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)

3252 / 1 = 3252 (the remainder is 0, so 1 is a divisor of 3252)
3252 / 2 = 1626 (the remainder is 0, so 2 is a divisor of 3252)
3252 / 3 = 1084 (the remainder is 0, so 3 is a divisor of 3252)
...
3252 / 3251 = 1.0003075976623 (the remainder is 1, so 3251 is not a divisor of 3252)
3252 / 3252 = 1 (the remainder is 0, so 3252 is a divisor of 3252)

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 3252 (i.e. 57.026309717533). 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 $\frac{N}{d} = D$ )

3252 / 1 = 3252 (the remainder is 0, so 1 and 3252 are divisors of 3252)
3252 / 2 = 1626 (the remainder is 0, so 2 and 1626 are divisors of 3252)
3252 / 3 = 1084 (the remainder is 0, so 3 and 1084 are divisors of 3252)
...
3252 / 56 = 58.071428571429 (the remainder is 4, so 56 is not a divisor of 3252)
3252 / 57 = 57.052631578947 (the remainder is 3, so 57 is not a divisor of 3252)