What are the divisors of 6001?

1, 17, 353, 6001

There is a total of 4 positive divisors.
The sum of these divisors is 6372.
The arithmetic mean is 1593.

4 odd divisors

1, 17, 353, 6001

How to compute the divisors of 6001?

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 6001 by each of the numbers from 1 to 6001 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)

6001 / 1 = 6001 (the remainder is 0, so 1 is a divisor of 6001)
6001 / 2 = 3000.5 (the remainder is 1, so 2 is not a divisor of 6001)
6001 / 3 = 2000.3333333333 (the remainder is 1, so 3 is not a divisor of 6001)
...
6001 / 6000 = 1.0001666666667 (the remainder is 1, so 6000 is not a divisor of 6001)
6001 / 6001 = 1 (the remainder is 0, so 6001 is a divisor of 6001)

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 6001 (i.e. 77.466121627457). 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 $\frac{N}{d} = D$ )

6001 / 1 = 6001 (the remainder is 0, so 1 and 6001 are divisors of 6001)
6001 / 2 = 3000.5 (the remainder is 1, so 2 is not a divisor of 6001)
6001 / 3 = 2000.3333333333 (the remainder is 1, so 3 is not a divisor of 6001)
...
6001 / 76 = 78.960526315789 (the remainder is 73, so 76 is not a divisor of 6001)
6001 / 77 = 77.935064935065 (the remainder is 72, so 77 is not a divisor of 6001)