What are the divisors of 6024?

1, 2, 3, 4, 6, 8, 12, 24, 251, 502, 753, 1004, 1506, 2008, 3012, 6024

There is a total of 16 positive divisors.
The sum of these divisors is 15120.
The arithmetic mean is 945.

12 even divisors

2, 4, 6, 8, 12, 24, 502, 1004, 1506, 2008, 3012, 6024

4 odd divisors

1, 3, 251, 753

How to compute the divisors of 6024?

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 6024 by each of the numbers from 1 to 6024 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)

6024 / 1 = 6024 (the remainder is 0, so 1 is a divisor of 6024)
6024 / 2 = 3012 (the remainder is 0, so 2 is a divisor of 6024)
6024 / 3 = 2008 (the remainder is 0, so 3 is a divisor of 6024)
...
6024 / 6023 = 1.0001660302175 (the remainder is 1, so 6023 is not a divisor of 6024)
6024 / 6024 = 1 (the remainder is 0, so 6024 is a divisor of 6024)

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 6024 (i.e. 77.614431647729). 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 $\frac{N}{d} = D$ )

6024 / 1 = 6024 (the remainder is 0, so 1 and 6024 are divisors of 6024)
6024 / 2 = 3012 (the remainder is 0, so 2 and 3012 are divisors of 6024)
6024 / 3 = 2008 (the remainder is 0, so 3 and 2008 are divisors of 6024)
...
6024 / 76 = 79.263157894737 (the remainder is 20, so 76 is not a divisor of 6024)
6024 / 77 = 78.233766233766 (the remainder is 18, so 77 is not a divisor of 6024)