What are the divisors of 6096?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 127, 254, 381, 508, 762, 1016, 1524, 2032, 3048, 6096

There is a total of 20 positive divisors.
The sum of these divisors is 15872.
The arithmetic mean is 793.6.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 254, 508, 762, 1016, 1524, 2032, 3048, 6096

4 odd divisors

1, 3, 127, 381

How to compute the divisors of 6096?

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 6096 by each of the numbers from 1 to 6096 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)

6096 / 1 = 6096 (the remainder is 0, so 1 is a divisor of 6096)
6096 / 2 = 3048 (the remainder is 0, so 2 is a divisor of 6096)
6096 / 3 = 2032 (the remainder is 0, so 3 is a divisor of 6096)
...
6096 / 6095 = 1.0001640689089 (the remainder is 1, so 6095 is not a divisor of 6096)
6096 / 6096 = 1 (the remainder is 0, so 6096 is a divisor of 6096)

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 6096 (i.e. 78.076885183773). 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 $\frac{N}{d} = D$ )

6096 / 1 = 6096 (the remainder is 0, so 1 and 6096 are divisors of 6096)
6096 / 2 = 3048 (the remainder is 0, so 2 and 3048 are divisors of 6096)
6096 / 3 = 2032 (the remainder is 0, so 3 and 2032 are divisors of 6096)
...
6096 / 77 = 79.168831168831 (the remainder is 13, so 77 is not a divisor of 6096)
6096 / 78 = 78.153846153846 (the remainder is 12, so 78 is not a divisor of 6096)