What are the divisors of 6084?

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 169, 234, 338, 468, 507, 676, 1014, 1521, 2028, 3042, 6084

There is a total of 27 positive divisors.
The sum of these divisors is 16653.
The arithmetic mean is 616.77777777778.

18 even divisors

2, 4, 6, 12, 18, 26, 36, 52, 78, 156, 234, 338, 468, 676, 1014, 2028, 3042, 6084

9 odd divisors

1, 3, 9, 13, 39, 117, 169, 507, 1521

How to compute the divisors of 6084?

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 6084 by each of the numbers from 1 to 6084 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)

6084 / 1 = 6084 (the remainder is 0, so 1 is a divisor of 6084)
6084 / 2 = 3042 (the remainder is 0, so 2 is a divisor of 6084)
6084 / 3 = 2028 (the remainder is 0, so 3 is a divisor of 6084)
...
6084 / 6083 = 1.0001643925695 (the remainder is 1, so 6083 is not a divisor of 6084)
6084 / 6084 = 1 (the remainder is 0, so 6084 is a divisor of 6084)

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 6084 (i.e. 78). 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 $\frac{N}{d} = D$ )

6084 / 1 = 6084 (the remainder is 0, so 1 and 6084 are divisors of 6084)
6084 / 2 = 3042 (the remainder is 0, so 2 and 3042 are divisors of 6084)
6084 / 3 = 2028 (the remainder is 0, so 3 and 2028 are divisors of 6084)
...
6084 / 77 = 79.012987012987 (the remainder is 1, so 77 is not a divisor of 6084)
6084 / 78 = 78 (the remainder is 0, so 78 and 78 are divisors of 6084)