What are the divisors of 6007?

1, 6007

There is a total of 2 positive divisors.
The sum of these divisors is 6008.
The arithmetic mean is 3004.

2 odd divisors

1, 6007

How to compute the divisors of 6007?

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 6007 by each of the numbers from 1 to 6007 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)

6007 / 1 = 6007 (the remainder is 0, so 1 is a divisor of 6007)
6007 / 2 = 3003.5 (the remainder is 1, so 2 is not a divisor of 6007)
6007 / 3 = 2002.3333333333 (the remainder is 1, so 3 is not a divisor of 6007)
...
6007 / 6006 = 1.0001665001665 (the remainder is 1, so 6006 is not a divisor of 6007)
6007 / 6007 = 1 (the remainder is 0, so 6007 is a divisor of 6007)

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 6007 (i.e. 77.504838558635). 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 $\frac{N}{d} = D$ )

6007 / 1 = 6007 (the remainder is 0, so 1 and 6007 are divisors of 6007)
6007 / 2 = 3003.5 (the remainder is 1, so 2 is not a divisor of 6007)
6007 / 3 = 2002.3333333333 (the remainder is 1, so 3 is not a divisor of 6007)
...
6007 / 76 = 79.039473684211 (the remainder is 3, so 76 is not a divisor of 6007)
6007 / 77 = 78.012987012987 (the remainder is 1, so 77 is not a divisor of 6007)