What are the divisors of 6082?

1, 2, 3041, 6082

There is a total of 4 positive divisors.
The sum of these divisors is 9126.
The arithmetic mean is 2281.5.

2 even divisors

2, 6082

2 odd divisors

1, 3041

How to compute the divisors of 6082?

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 6082 by each of the numbers from 1 to 6082 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)

6082 / 1 = 6082 (the remainder is 0, so 1 is a divisor of 6082)
6082 / 2 = 3041 (the remainder is 0, so 2 is a divisor of 6082)
6082 / 3 = 2027.3333333333 (the remainder is 1, so 3 is not a divisor of 6082)
...
6082 / 6081 = 1.0001644466371 (the remainder is 1, so 6081 is not a divisor of 6082)
6082 / 6082 = 1 (the remainder is 0, so 6082 is a divisor of 6082)

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 6082 (i.e. 77.987178433381). 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 $\frac{N}{d} = D$ )

6082 / 1 = 6082 (the remainder is 0, so 1 and 6082 are divisors of 6082)
6082 / 2 = 3041 (the remainder is 0, so 2 and 3041 are divisors of 6082)
6082 / 3 = 2027.3333333333 (the remainder is 1, so 3 is not a divisor of 6082)
...
6082 / 76 = 80.026315789474 (the remainder is 2, so 76 is not a divisor of 6082)
6082 / 77 = 78.987012987013 (the remainder is 76, so 77 is not a divisor of 6082)