What are the divisors of 3036?

1, 2, 3, 4, 6, 11, 12, 22, 23, 33, 44, 46, 66, 69, 92, 132, 138, 253, 276, 506, 759, 1012, 1518, 3036

There is a total of 24 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 336.

16 even divisors

2, 4, 6, 12, 22, 44, 46, 66, 92, 132, 138, 276, 506, 1012, 1518, 3036

8 odd divisors

1, 3, 11, 23, 33, 69, 253, 759

How to compute the divisors of 3036?

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 3036 by each of the numbers from 1 to 3036 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)

3036 / 1 = 3036 (the remainder is 0, so 1 is a divisor of 3036)
3036 / 2 = 1518 (the remainder is 0, so 2 is a divisor of 3036)
3036 / 3 = 1012 (the remainder is 0, so 3 is a divisor of 3036)
...
3036 / 3035 = 1.0003294892916 (the remainder is 1, so 3035 is not a divisor of 3036)
3036 / 3036 = 1 (the remainder is 0, so 3036 is a divisor of 3036)

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 3036 (i.e. 55.099909255824). 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 $\frac{N}{d} = D$ )

3036 / 1 = 3036 (the remainder is 0, so 1 and 3036 are divisors of 3036)
3036 / 2 = 1518 (the remainder is 0, so 2 and 1518 are divisors of 3036)
3036 / 3 = 1012 (the remainder is 0, so 3 and 1012 are divisors of 3036)
...
3036 / 54 = 56.222222222222 (the remainder is 12, so 54 is not a divisor of 3036)
3036 / 55 = 55.2 (the remainder is 11, so 55 is not a divisor of 3036)