What are the divisors of 9003?

1, 3, 3001, 9003

There is a total of 4 positive divisors.
The sum of these divisors is 12008.
The arithmetic mean is 3002.

4 odd divisors

1, 3, 3001, 9003

How to compute the divisors of 9003?

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 9003 by each of the numbers from 1 to 9003 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)

9003 / 1 = 9003 (the remainder is 0, so 1 is a divisor of 9003)
9003 / 2 = 4501.5 (the remainder is 1, so 2 is not a divisor of 9003)
9003 / 3 = 3001 (the remainder is 0, so 3 is a divisor of 9003)
...
9003 / 9002 = 1.0001110864252 (the remainder is 1, so 9002 is not a divisor of 9003)
9003 / 9003 = 1 (the remainder is 0, so 9003 is a divisor of 9003)

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 9003 (i.e. 94.884139875956). 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 $\frac{N}{d} = D$ )

9003 / 1 = 9003 (the remainder is 0, so 1 and 9003 are divisors of 9003)
9003 / 2 = 4501.5 (the remainder is 1, so 2 is not a divisor of 9003)
9003 / 3 = 3001 (the remainder is 0, so 3 and 3001 are divisors of 9003)
...
9003 / 93 = 96.806451612903 (the remainder is 75, so 93 is not a divisor of 9003)
9003 / 94 = 95.776595744681 (the remainder is 73, so 94 is not a divisor of 9003)