What are the divisors of 9005?

1, 5, 1801, 9005

There is a total of 4 positive divisors.
The sum of these divisors is 10812.
The arithmetic mean is 2703.

4 odd divisors

1, 5, 1801, 9005

How to compute the divisors of 9005?

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 9005 by each of the numbers from 1 to 9005 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)

9005 / 1 = 9005 (the remainder is 0, so 1 is a divisor of 9005)
9005 / 2 = 4502.5 (the remainder is 1, so 2 is not a divisor of 9005)
9005 / 3 = 3001.6666666667 (the remainder is 2, so 3 is not a divisor of 9005)
...
9005 / 9004 = 1.0001110617503 (the remainder is 1, so 9004 is not a divisor of 9005)
9005 / 9005 = 1 (the remainder is 0, so 9005 is a divisor of 9005)

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 9005 (i.e. 94.894678459859). 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 $\frac{N}{d} = D$ )

9005 / 1 = 9005 (the remainder is 0, so 1 and 9005 are divisors of 9005)
9005 / 2 = 4502.5 (the remainder is 1, so 2 is not a divisor of 9005)
9005 / 3 = 3001.6666666667 (the remainder is 2, so 3 is not a divisor of 9005)
...
9005 / 93 = 96.827956989247 (the remainder is 77, so 93 is not a divisor of 9005)
9005 / 94 = 95.797872340426 (the remainder is 75, so 94 is not a divisor of 9005)