What are the divisors of 6081?

1, 3, 2027, 6081

There is a total of 4 positive divisors.
The sum of these divisors is 8112.
The arithmetic mean is 2028.

4 odd divisors

1, 3, 2027, 6081

How to compute the divisors of 6081?

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 6081 by each of the numbers from 1 to 6081 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)

6081 / 1 = 6081 (the remainder is 0, so 1 is a divisor of 6081)
6081 / 2 = 3040.5 (the remainder is 1, so 2 is not a divisor of 6081)
6081 / 3 = 2027 (the remainder is 0, so 3 is a divisor of 6081)
...
6081 / 6080 = 1.0001644736842 (the remainder is 1, so 6080 is not a divisor of 6081)
6081 / 6081 = 1 (the remainder is 0, so 6081 is a divisor of 6081)

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 6081 (i.e. 77.980766859528). 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 $\frac{N}{d} = D$ )

6081 / 1 = 6081 (the remainder is 0, so 1 and 6081 are divisors of 6081)
6081 / 2 = 3040.5 (the remainder is 1, so 2 is not a divisor of 6081)
6081 / 3 = 2027 (the remainder is 0, so 3 and 2027 are divisors of 6081)
...
6081 / 76 = 80.013157894737 (the remainder is 1, so 76 is not a divisor of 6081)
6081 / 77 = 78.974025974026 (the remainder is 75, so 77 is not a divisor of 6081)