What are the divisors of 8006?

1, 2, 4003, 8006

There is a total of 4 positive divisors.
The sum of these divisors is 12012.
The arithmetic mean is 3003.

2 even divisors

2, 8006

2 odd divisors

1, 4003

How to compute the divisors of 8006?

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 8006 by each of the numbers from 1 to 8006 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)

8006 / 1 = 8006 (the remainder is 0, so 1 is a divisor of 8006)
8006 / 2 = 4003 (the remainder is 0, so 2 is a divisor of 8006)
8006 / 3 = 2668.6666666667 (the remainder is 2, so 3 is not a divisor of 8006)
...
8006 / 8005 = 1.0001249219238 (the remainder is 1, so 8005 is not a divisor of 8006)
8006 / 8006 = 1 (the remainder is 0, so 8006 is a divisor of 8006)

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 8006 (i.e. 89.47625383307). 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 $\frac{N}{d} = D$ )

8006 / 1 = 8006 (the remainder is 0, so 1 and 8006 are divisors of 8006)
8006 / 2 = 4003 (the remainder is 0, so 2 and 4003 are divisors of 8006)
8006 / 3 = 2668.6666666667 (the remainder is 2, so 3 is not a divisor of 8006)
...
8006 / 88 = 90.977272727273 (the remainder is 86, so 88 is not a divisor of 8006)
8006 / 89 = 89.955056179775 (the remainder is 85, so 89 is not a divisor of 8006)