What are the divisors of 9068?

1, 2, 4, 2267, 4534, 9068

There is a total of 6 positive divisors.
The sum of these divisors is 15876.
The arithmetic mean is 2646.

4 even divisors

2, 4, 4534, 9068

2 odd divisors

1, 2267

How to compute the divisors of 9068?

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 9068 by each of the numbers from 1 to 9068 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)

9068 / 1 = 9068 (the remainder is 0, so 1 is a divisor of 9068)
9068 / 2 = 4534 (the remainder is 0, so 2 is a divisor of 9068)
9068 / 3 = 3022.6666666667 (the remainder is 2, so 3 is not a divisor of 9068)
...
9068 / 9067 = 1.0001102900629 (the remainder is 1, so 9067 is not a divisor of 9068)
9068 / 9068 = 1 (the remainder is 0, so 9068 is a divisor of 9068)

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 9068 (i.e. 95.226046856939). 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 $\frac{N}{d} = D$ )

9068 / 1 = 9068 (the remainder is 0, so 1 and 9068 are divisors of 9068)
9068 / 2 = 4534 (the remainder is 0, so 2 and 4534 are divisors of 9068)
9068 / 3 = 3022.6666666667 (the remainder is 2, so 3 is not a divisor of 9068)
...
9068 / 94 = 96.468085106383 (the remainder is 44, so 94 is not a divisor of 9068)
9068 / 95 = 95.452631578947 (the remainder is 43, so 95 is not a divisor of 9068)