What are the divisors of 6009?

1, 3, 2003, 6009

There is a total of 4 positive divisors.
The sum of these divisors is 8016.
The arithmetic mean is 2004.

4 odd divisors

1, 3, 2003, 6009

How to compute the divisors of 6009?

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 6009 by each of the numbers from 1 to 6009 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)

6009 / 1 = 6009 (the remainder is 0, so 1 is a divisor of 6009)
6009 / 2 = 3004.5 (the remainder is 1, so 2 is not a divisor of 6009)
6009 / 3 = 2003 (the remainder is 0, so 3 is a divisor of 6009)
...
6009 / 6008 = 1.0001664447403 (the remainder is 1, so 6008 is not a divisor of 6009)
6009 / 6009 = 1 (the remainder is 0, so 6009 is a divisor of 6009)

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 6009 (i.e. 77.517739905134). 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 $\frac{N}{d} = D$ )

6009 / 1 = 6009 (the remainder is 0, so 1 and 6009 are divisors of 6009)
6009 / 2 = 3004.5 (the remainder is 1, so 2 is not a divisor of 6009)
6009 / 3 = 2003 (the remainder is 0, so 3 and 2003 are divisors of 6009)
...
6009 / 76 = 79.065789473684 (the remainder is 5, so 76 is not a divisor of 6009)
6009 / 77 = 78.038961038961 (the remainder is 3, so 77 is not a divisor of 6009)