What are the divisors of 6065?

1, 5, 1213, 6065

There is a total of 4 positive divisors.
The sum of these divisors is 7284.
The arithmetic mean is 1821.

4 odd divisors

1, 5, 1213, 6065

How to compute the divisors of 6065?

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 6065 by each of the numbers from 1 to 6065 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)

6065 / 1 = 6065 (the remainder is 0, so 1 is a divisor of 6065)
6065 / 2 = 3032.5 (the remainder is 1, so 2 is not a divisor of 6065)
6065 / 3 = 2021.6666666667 (the remainder is 2, so 3 is not a divisor of 6065)
...
6065 / 6064 = 1.0001649076517 (the remainder is 1, so 6064 is not a divisor of 6065)
6065 / 6065 = 1 (the remainder is 0, so 6065 is a divisor of 6065)

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 6065 (i.e. 77.87810988975). 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 $\frac{N}{d} = D$ )

6065 / 1 = 6065 (the remainder is 0, so 1 and 6065 are divisors of 6065)
6065 / 2 = 3032.5 (the remainder is 1, so 2 is not a divisor of 6065)
6065 / 3 = 2021.6666666667 (the remainder is 2, so 3 is not a divisor of 6065)
...
6065 / 76 = 79.802631578947 (the remainder is 61, so 76 is not a divisor of 6065)
6065 / 77 = 78.766233766234 (the remainder is 59, so 77 is not a divisor of 6065)