What are the divisors of 3024?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 36, 42, 48, 54, 56, 63, 72, 84, 108, 112, 126, 144, 168, 189, 216, 252, 336, 378, 432, 504, 756, 1008, 1512, 3024

There is a total of 40 positive divisors.
The sum of these divisors is 9920.
The arithmetic mean is 248.

32 even divisors

2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 36, 42, 48, 54, 56, 72, 84, 108, 112, 126, 144, 168, 216, 252, 336, 378, 432, 504, 756, 1008, 1512, 3024

8 odd divisors

1, 3, 7, 9, 21, 27, 63, 189

How to compute the divisors of 3024?

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 3024 by each of the numbers from 1 to 3024 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)

3024 / 1 = 3024 (the remainder is 0, so 1 is a divisor of 3024)
3024 / 2 = 1512 (the remainder is 0, so 2 is a divisor of 3024)
3024 / 3 = 1008 (the remainder is 0, so 3 is a divisor of 3024)
...
3024 / 3023 = 1.0003307972213 (the remainder is 1, so 3023 is not a divisor of 3024)
3024 / 3024 = 1 (the remainder is 0, so 3024 is a divisor of 3024)

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 3024 (i.e. 54.99090833947). 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 $\frac{N}{d} = D$ )

3024 / 1 = 3024 (the remainder is 0, so 1 and 3024 are divisors of 3024)
3024 / 2 = 1512 (the remainder is 0, so 2 and 1512 are divisors of 3024)
3024 / 3 = 1008 (the remainder is 0, so 3 and 1008 are divisors of 3024)
...
3024 / 53 = 57.056603773585 (the remainder is 3, so 53 is not a divisor of 3024)
3024 / 54 = 56 (the remainder is 0, so 54 and 56 are divisors of 3024)