What are the divisors of 6005?

1, 5, 1201, 6005

There is a total of 4 positive divisors.
The sum of these divisors is 7212.
The arithmetic mean is 1803.

4 odd divisors

1, 5, 1201, 6005

How to compute the divisors of 6005?

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 6005 by each of the numbers from 1 to 6005 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)

6005 / 1 = 6005 (the remainder is 0, so 1 is a divisor of 6005)
6005 / 2 = 3002.5 (the remainder is 1, so 2 is not a divisor of 6005)
6005 / 3 = 2001.6666666667 (the remainder is 2, so 3 is not a divisor of 6005)
...
6005 / 6004 = 1.0001665556296 (the remainder is 1, so 6004 is not a divisor of 6005)
6005 / 6005 = 1 (the remainder is 0, so 6005 is a divisor of 6005)

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 6005 (i.e. 77.491935064237). 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 $\frac{N}{d} = D$ )

6005 / 1 = 6005 (the remainder is 0, so 1 and 6005 are divisors of 6005)
6005 / 2 = 3002.5 (the remainder is 1, so 2 is not a divisor of 6005)
6005 / 3 = 2001.6666666667 (the remainder is 2, so 3 is not a divisor of 6005)
...
6005 / 76 = 79.013157894737 (the remainder is 1, so 76 is not a divisor of 6005)
6005 / 77 = 77.987012987013 (the remainder is 76, so 77 is not a divisor of 6005)