What are the divisors of 6086?

1, 2, 17, 34, 179, 358, 3043, 6086

There is a total of 8 positive divisors.
The sum of these divisors is 9720.
The arithmetic mean is 1215.

4 even divisors

2, 34, 358, 6086

4 odd divisors

1, 17, 179, 3043

How to compute the divisors of 6086?

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 6086 by each of the numbers from 1 to 6086 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)

6086 / 1 = 6086 (the remainder is 0, so 1 is a divisor of 6086)
6086 / 2 = 3043 (the remainder is 0, so 2 is a divisor of 6086)
6086 / 3 = 2028.6666666667 (the remainder is 2, so 3 is not a divisor of 6086)
...
6086 / 6085 = 1.0001643385374 (the remainder is 1, so 6085 is not a divisor of 6086)
6086 / 6086 = 1 (the remainder is 0, so 6086 is a divisor of 6086)

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 6086 (i.e. 78.012819459368). 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 $\frac{N}{d} = D$ )

6086 / 1 = 6086 (the remainder is 0, so 1 and 6086 are divisors of 6086)
6086 / 2 = 3043 (the remainder is 0, so 2 and 3043 are divisors of 6086)
6086 / 3 = 2028.6666666667 (the remainder is 2, so 3 is not a divisor of 6086)
...
6086 / 77 = 79.038961038961 (the remainder is 3, so 77 is not a divisor of 6086)
6086 / 78 = 78.025641025641 (the remainder is 2, so 78 is not a divisor of 6086)