What are the divisors of 6048?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 54, 56, 63, 72, 84, 96, 108, 112, 126, 144, 168, 189, 216, 224, 252, 288, 336, 378, 432, 504, 672, 756, 864, 1008, 1512, 2016, 3024, 6048

There is a total of 48 positive divisors.
The sum of these divisors is 20160.
The arithmetic mean is 420.

40 even divisors

2, 4, 6, 8, 12, 14, 16, 18, 24, 28, 32, 36, 42, 48, 54, 56, 72, 84, 96, 108, 112, 126, 144, 168, 216, 224, 252, 288, 336, 378, 432, 504, 672, 756, 864, 1008, 1512, 2016, 3024, 6048

8 odd divisors

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

How to compute the divisors of 6048?

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 6048 by each of the numbers from 1 to 6048 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)

6048 / 1 = 6048 (the remainder is 0, so 1 is a divisor of 6048)
6048 / 2 = 3024 (the remainder is 0, so 2 is a divisor of 6048)
6048 / 3 = 2016 (the remainder is 0, so 3 is a divisor of 6048)
...
6048 / 6047 = 1.0001653712585 (the remainder is 1, so 6047 is not a divisor of 6048)
6048 / 6048 = 1 (the remainder is 0, so 6048 is a divisor of 6048)

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 6048 (i.e. 77.768888380894). 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 $\frac{N}{d} = D$ )

6048 / 1 = 6048 (the remainder is 0, so 1 and 6048 are divisors of 6048)
6048 / 2 = 3024 (the remainder is 0, so 2 and 3024 are divisors of 6048)
6048 / 3 = 2016 (the remainder is 0, so 3 and 2016 are divisors of 6048)
...
6048 / 76 = 79.578947368421 (the remainder is 44, so 76 is not a divisor of 6048)
6048 / 77 = 78.545454545455 (the remainder is 42, so 77 is not a divisor of 6048)