What are the divisors of 6006?

1, 2, 3, 6, 7, 11, 13, 14, 21, 22, 26, 33, 39, 42, 66, 77, 78, 91, 143, 154, 182, 231, 273, 286, 429, 462, 546, 858, 1001, 2002, 3003, 6006

There is a total of 32 positive divisors.
The sum of these divisors is 16128.
The arithmetic mean is 504.

16 even divisors

2, 6, 14, 22, 26, 42, 66, 78, 154, 182, 286, 462, 546, 858, 2002, 6006

16 odd divisors

1, 3, 7, 11, 13, 21, 33, 39, 77, 91, 143, 231, 273, 429, 1001, 3003

How to compute the divisors of 6006?

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 6006 by each of the numbers from 1 to 6006 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)

6006 / 1 = 6006 (the remainder is 0, so 1 is a divisor of 6006)
6006 / 2 = 3003 (the remainder is 0, so 2 is a divisor of 6006)
6006 / 3 = 2002 (the remainder is 0, so 3 is a divisor of 6006)
...
6006 / 6005 = 1.0001665278934 (the remainder is 1, so 6005 is not a divisor of 6006)
6006 / 6006 = 1 (the remainder is 0, so 6006 is a divisor of 6006)

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 6006 (i.e. 77.49838707999). 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 $\frac{N}{d} = D$ )

6006 / 1 = 6006 (the remainder is 0, so 1 and 6006 are divisors of 6006)
6006 / 2 = 3003 (the remainder is 0, so 2 and 3003 are divisors of 6006)
6006 / 3 = 2002 (the remainder is 0, so 3 and 2002 are divisors of 6006)
...
6006 / 76 = 79.026315789474 (the remainder is 2, so 76 is not a divisor of 6006)
6006 / 77 = 78 (the remainder is 0, so 77 and 78 are divisors of 6006)