What are the divisors of 6085?

1, 5, 1217, 6085

There is a total of 4 positive divisors.
The sum of these divisors is 7308.
The arithmetic mean is 1827.

4 odd divisors

1, 5, 1217, 6085

How to compute the divisors of 6085?

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 6085 by each of the numbers from 1 to 6085 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)

6085 / 1 = 6085 (the remainder is 0, so 1 is a divisor of 6085)
6085 / 2 = 3042.5 (the remainder is 1, so 2 is not a divisor of 6085)
6085 / 3 = 2028.3333333333 (the remainder is 1, so 3 is not a divisor of 6085)
...
6085 / 6084 = 1.000164365549 (the remainder is 1, so 6084 is not a divisor of 6085)
6085 / 6085 = 1 (the remainder is 0, so 6085 is a divisor of 6085)

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 6085 (i.e. 78.006409993026). 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 $\frac{N}{d} = D$ )

6085 / 1 = 6085 (the remainder is 0, so 1 and 6085 are divisors of 6085)
6085 / 2 = 3042.5 (the remainder is 1, so 2 is not a divisor of 6085)
6085 / 3 = 2028.3333333333 (the remainder is 1, so 3 is not a divisor of 6085)
...
6085 / 77 = 79.025974025974 (the remainder is 2, so 77 is not a divisor of 6085)
6085 / 78 = 78.012820512821 (the remainder is 1, so 78 is not a divisor of 6085)