What are the divisors of 6017?

1, 11, 547, 6017

There is a total of 4 positive divisors.
The sum of these divisors is 6576.
The arithmetic mean is 1644.

4 odd divisors

1, 11, 547, 6017

How to compute the divisors of 6017?

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 6017 by each of the numbers from 1 to 6017 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)

6017 / 1 = 6017 (the remainder is 0, so 1 is a divisor of 6017)
6017 / 2 = 3008.5 (the remainder is 1, so 2 is not a divisor of 6017)
6017 / 3 = 2005.6666666667 (the remainder is 2, so 3 is not a divisor of 6017)
...
6017 / 6016 = 1.0001662234043 (the remainder is 1, so 6016 is not a divisor of 6017)
6017 / 6017 = 1 (the remainder is 0, so 6017 is a divisor of 6017)

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 6017 (i.e. 77.569323833588). 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 $\frac{N}{d} = D$ )

6017 / 1 = 6017 (the remainder is 0, so 1 and 6017 are divisors of 6017)
6017 / 2 = 3008.5 (the remainder is 1, so 2 is not a divisor of 6017)
6017 / 3 = 2005.6666666667 (the remainder is 2, so 3 is not a divisor of 6017)
...
6017 / 76 = 79.171052631579 (the remainder is 13, so 76 is not a divisor of 6017)
6017 / 77 = 78.142857142857 (the remainder is 11, so 77 is not a divisor of 6017)