What are the divisors of 3228?

1, 2, 3, 4, 6, 12, 269, 538, 807, 1076, 1614, 3228

There is a total of 12 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 630.

8 even divisors

2, 4, 6, 12, 538, 1076, 1614, 3228

4 odd divisors

1, 3, 269, 807

How to compute the divisors of 3228?

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 3228 by each of the numbers from 1 to 3228 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)

3228 / 1 = 3228 (the remainder is 0, so 1 is a divisor of 3228)
3228 / 2 = 1614 (the remainder is 0, so 2 is a divisor of 3228)
3228 / 3 = 1076 (the remainder is 0, so 3 is a divisor of 3228)
...
3228 / 3227 = 1.0003098853424 (the remainder is 1, so 3227 is not a divisor of 3228)
3228 / 3228 = 1 (the remainder is 0, so 3228 is a divisor of 3228)

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 3228 (i.e. 56.815490845367). 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 $\frac{N}{d} = D$ )

3228 / 1 = 3228 (the remainder is 0, so 1 and 3228 are divisors of 3228)
3228 / 2 = 1614 (the remainder is 0, so 2 and 1614 are divisors of 3228)
3228 / 3 = 1076 (the remainder is 0, so 3 and 1076 are divisors of 3228)
...
3228 / 55 = 58.690909090909 (the remainder is 38, so 55 is not a divisor of 3228)
3228 / 56 = 57.642857142857 (the remainder is 36, so 56 is not a divisor of 3228)