What are the divisors of 3096?

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 43, 72, 86, 129, 172, 258, 344, 387, 516, 774, 1032, 1548, 3096

There is a total of 24 positive divisors.
The sum of these divisors is 8580.
The arithmetic mean is 357.5.

18 even divisors

2, 4, 6, 8, 12, 18, 24, 36, 72, 86, 172, 258, 344, 516, 774, 1032, 1548, 3096

6 odd divisors

1, 3, 9, 43, 129, 387

How to compute the divisors of 3096?

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 3096 by each of the numbers from 1 to 3096 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)

3096 / 1 = 3096 (the remainder is 0, so 1 is a divisor of 3096)
3096 / 2 = 1548 (the remainder is 0, so 2 is a divisor of 3096)
3096 / 3 = 1032 (the remainder is 0, so 3 is a divisor of 3096)
...
3096 / 3095 = 1.0003231017771 (the remainder is 1, so 3095 is not a divisor of 3096)
3096 / 3096 = 1 (the remainder is 0, so 3096 is a divisor of 3096)

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 3096 (i.e. 55.641710972974). 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 $\frac{N}{d} = D$ )

3096 / 1 = 3096 (the remainder is 0, so 1 and 3096 are divisors of 3096)
3096 / 2 = 1548 (the remainder is 0, so 2 and 1548 are divisors of 3096)
3096 / 3 = 1032 (the remainder is 0, so 3 and 1032 are divisors of 3096)
...
3096 / 54 = 57.333333333333 (the remainder is 18, so 54 is not a divisor of 3096)
3096 / 55 = 56.290909090909 (the remainder is 16, so 55 is not a divisor of 3096)