What are the divisors of 9085?

1, 5, 23, 79, 115, 395, 1817, 9085

There is a total of 8 positive divisors.
The sum of these divisors is 11520.
The arithmetic mean is 1440.

8 odd divisors

1, 5, 23, 79, 115, 395, 1817, 9085

How to compute the divisors of 9085?

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 9085 by each of the numbers from 1 to 9085 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)

9085 / 1 = 9085 (the remainder is 0, so 1 is a divisor of 9085)
9085 / 2 = 4542.5 (the remainder is 1, so 2 is not a divisor of 9085)
9085 / 3 = 3028.3333333333 (the remainder is 1, so 3 is not a divisor of 9085)
...
9085 / 9084 = 1.0001100836636 (the remainder is 1, so 9084 is not a divisor of 9085)
9085 / 9085 = 1 (the remainder is 0, so 9085 is a divisor of 9085)

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 9085 (i.e. 95.315266353297). 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 $\frac{N}{d} = D$ )

9085 / 1 = 9085 (the remainder is 0, so 1 and 9085 are divisors of 9085)
9085 / 2 = 4542.5 (the remainder is 1, so 2 is not a divisor of 9085)
9085 / 3 = 3028.3333333333 (the remainder is 1, so 3 is not a divisor of 9085)
...
9085 / 94 = 96.648936170213 (the remainder is 61, so 94 is not a divisor of 9085)
9085 / 95 = 95.631578947368 (the remainder is 60, so 95 is not a divisor of 9085)