What are the divisors of 3084?

1, 2, 3, 4, 6, 12, 257, 514, 771, 1028, 1542, 3084

There is a total of 12 positive divisors.
The sum of these divisors is 7224.
The arithmetic mean is 602.

8 even divisors

2, 4, 6, 12, 514, 1028, 1542, 3084

4 odd divisors

1, 3, 257, 771

How to compute the divisors of 3084?

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 3084 by each of the numbers from 1 to 3084 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)

3084 / 1 = 3084 (the remainder is 0, so 1 is a divisor of 3084)
3084 / 2 = 1542 (the remainder is 0, so 2 is a divisor of 3084)
3084 / 3 = 1028 (the remainder is 0, so 3 is a divisor of 3084)
...
3084 / 3083 = 1.0003243593902 (the remainder is 1, so 3083 is not a divisor of 3084)
3084 / 3084 = 1 (the remainder is 0, so 3084 is a divisor of 3084)

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 3084 (i.e. 55.533773507659). 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 $\frac{N}{d} = D$ )

3084 / 1 = 3084 (the remainder is 0, so 1 and 3084 are divisors of 3084)
3084 / 2 = 1542 (the remainder is 0, so 2 and 1542 are divisors of 3084)
3084 / 3 = 1028 (the remainder is 0, so 3 and 1028 are divisors of 3084)
...
3084 / 54 = 57.111111111111 (the remainder is 6, so 54 is not a divisor of 3084)
3084 / 55 = 56.072727272727 (the remainder is 4, so 55 is not a divisor of 3084)