What are the divisors of 6044?

1, 2, 4, 1511, 3022, 6044

There is a total of 6 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 1764.

4 even divisors

2, 4, 3022, 6044

2 odd divisors

1, 1511

How to compute the divisors of 6044?

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 6044 by each of the numbers from 1 to 6044 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)

6044 / 1 = 6044 (the remainder is 0, so 1 is a divisor of 6044)
6044 / 2 = 3022 (the remainder is 0, so 2 is a divisor of 6044)
6044 / 3 = 2014.6666666667 (the remainder is 2, so 3 is not a divisor of 6044)
...
6044 / 6043 = 1.0001654807215 (the remainder is 1, so 6043 is not a divisor of 6044)
6044 / 6044 = 1 (the remainder is 0, so 6044 is a divisor of 6044)

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 6044 (i.e. 77.743166902307). 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 $\frac{N}{d} = D$ )

6044 / 1 = 6044 (the remainder is 0, so 1 and 6044 are divisors of 6044)
6044 / 2 = 3022 (the remainder is 0, so 2 and 3022 are divisors of 6044)
6044 / 3 = 2014.6666666667 (the remainder is 2, so 3 is not a divisor of 6044)
...
6044 / 76 = 79.526315789474 (the remainder is 40, so 76 is not a divisor of 6044)
6044 / 77 = 78.493506493506 (the remainder is 38, so 77 is not a divisor of 6044)