What are the divisors of 9084?

1, 2, 3, 4, 6, 12, 757, 1514, 2271, 3028, 4542, 9084

There is a total of 12 positive divisors.
The sum of these divisors is 21224.
The arithmetic mean is 1768.6666666667.

8 even divisors

2, 4, 6, 12, 1514, 3028, 4542, 9084

4 odd divisors

1, 3, 757, 2271

How to compute the divisors of 9084?

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 9084 by each of the numbers from 1 to 9084 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)

9084 / 1 = 9084 (the remainder is 0, so 1 is a divisor of 9084)
9084 / 2 = 4542 (the remainder is 0, so 2 is a divisor of 9084)
9084 / 3 = 3028 (the remainder is 0, so 3 is a divisor of 9084)
...
9084 / 9083 = 1.0001100957833 (the remainder is 1, so 9083 is not a divisor of 9084)
9084 / 9084 = 1 (the remainder is 0, so 9084 is a divisor of 9084)

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 9084 (i.e. 95.310020459551). 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 $\frac{N}{d} = D$ )

9084 / 1 = 9084 (the remainder is 0, so 1 and 9084 are divisors of 9084)
9084 / 2 = 4542 (the remainder is 0, so 2 and 4542 are divisors of 9084)
9084 / 3 = 3028 (the remainder is 0, so 3 and 3028 are divisors of 9084)
...
9084 / 94 = 96.63829787234 (the remainder is 60, so 94 is not a divisor of 9084)
9084 / 95 = 95.621052631579 (the remainder is 59, so 95 is not a divisor of 9084)