What are the divisors of 9065?

1, 5, 7, 35, 37, 49, 185, 245, 259, 1295, 1813, 9065

There is a total of 12 positive divisors.
The sum of these divisors is 12996.
The arithmetic mean is 1083.

12 odd divisors

1, 5, 7, 35, 37, 49, 185, 245, 259, 1295, 1813, 9065

How to compute the divisors of 9065?

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 9065 by each of the numbers from 1 to 9065 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)

9065 / 1 = 9065 (the remainder is 0, so 1 is a divisor of 9065)
9065 / 2 = 4532.5 (the remainder is 1, so 2 is not a divisor of 9065)
9065 / 3 = 3021.6666666667 (the remainder is 2, so 3 is not a divisor of 9065)
...
9065 / 9064 = 1.0001103265666 (the remainder is 1, so 9064 is not a divisor of 9065)
9065 / 9065 = 1 (the remainder is 0, so 9065 is a divisor of 9065)

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 9065 (i.e. 95.210293561148). 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 $\frac{N}{d} = D$ )

9065 / 1 = 9065 (the remainder is 0, so 1 and 9065 are divisors of 9065)
9065 / 2 = 4532.5 (the remainder is 1, so 2 is not a divisor of 9065)
9065 / 3 = 3021.6666666667 (the remainder is 2, so 3 is not a divisor of 9065)
...
9065 / 94 = 96.436170212766 (the remainder is 41, so 94 is not a divisor of 9065)
9065 / 95 = 95.421052631579 (the remainder is 40, so 95 is not a divisor of 9065)