What are the divisors of 4044?

1, 2, 3, 4, 6, 12, 337, 674, 1011, 1348, 2022, 4044

There is a total of 12 positive divisors.
The sum of these divisors is 9464.
The arithmetic mean is 788.66666666667.

8 even divisors

2, 4, 6, 12, 674, 1348, 2022, 4044

4 odd divisors

1, 3, 337, 1011

How to compute the divisors of 4044?

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 4044 by each of the numbers from 1 to 4044 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)

4044 / 1 = 4044 (the remainder is 0, so 1 is a divisor of 4044)
4044 / 2 = 2022 (the remainder is 0, so 2 is a divisor of 4044)
4044 / 3 = 1348 (the remainder is 0, so 3 is a divisor of 4044)
...
4044 / 4043 = 1.0002473410834 (the remainder is 1, so 4043 is not a divisor of 4044)
4044 / 4044 = 1 (the remainder is 0, so 4044 is a divisor of 4044)

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 4044 (i.e. 63.592452382339). 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 $\frac{N}{d} = D$ )

4044 / 1 = 4044 (the remainder is 0, so 1 and 4044 are divisors of 4044)
4044 / 2 = 2022 (the remainder is 0, so 2 and 2022 are divisors of 4044)
4044 / 3 = 1348 (the remainder is 0, so 3 and 1348 are divisors of 4044)
...
4044 / 62 = 65.225806451613 (the remainder is 14, so 62 is not a divisor of 4044)
4044 / 63 = 64.190476190476 (the remainder is 12, so 63 is not a divisor of 4044)