What are the divisors of 9066?

1, 2, 3, 6, 1511, 3022, 4533, 9066

There is a total of 8 positive divisors.
The sum of these divisors is 18144.
The arithmetic mean is 2268.

4 even divisors

2, 6, 3022, 9066

4 odd divisors

1, 3, 1511, 4533

How to compute the divisors of 9066?

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 9066 by each of the numbers from 1 to 9066 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)

9066 / 1 = 9066 (the remainder is 0, so 1 is a divisor of 9066)
9066 / 2 = 4533 (the remainder is 0, so 2 is a divisor of 9066)
9066 / 3 = 3022 (the remainder is 0, so 3 is a divisor of 9066)
...
9066 / 9065 = 1.000110314396 (the remainder is 1, so 9065 is not a divisor of 9066)
9066 / 9066 = 1 (the remainder is 0, so 9066 is a divisor of 9066)

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 9066 (i.e. 95.215544949341). 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 $\frac{N}{d} = D$ )

9066 / 1 = 9066 (the remainder is 0, so 1 and 9066 are divisors of 9066)
9066 / 2 = 4533 (the remainder is 0, so 2 and 4533 are divisors of 9066)
9066 / 3 = 3022 (the remainder is 0, so 3 and 3022 are divisors of 9066)
...
9066 / 94 = 96.446808510638 (the remainder is 42, so 94 is not a divisor of 9066)
9066 / 95 = 95.431578947368 (the remainder is 41, so 95 is not a divisor of 9066)