What are the divisors of 6095?

1, 5, 23, 53, 115, 265, 1219, 6095

There is a total of 8 positive divisors.
The sum of these divisors is 7776.
The arithmetic mean is 972.

8 odd divisors

1, 5, 23, 53, 115, 265, 1219, 6095

How to compute the divisors of 6095?

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 6095 by each of the numbers from 1 to 6095 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)

6095 / 1 = 6095 (the remainder is 0, so 1 is a divisor of 6095)
6095 / 2 = 3047.5 (the remainder is 1, so 2 is not a divisor of 6095)
6095 / 3 = 2031.6666666667 (the remainder is 2, so 3 is not a divisor of 6095)
...
6095 / 6094 = 1.000164095832 (the remainder is 1, so 6094 is not a divisor of 6095)
6095 / 6095 = 1 (the remainder is 0, so 6095 is a divisor of 6095)

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 6095 (i.e. 78.070480977127). 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 $\frac{N}{d} = D$ )

6095 / 1 = 6095 (the remainder is 0, so 1 and 6095 are divisors of 6095)
6095 / 2 = 3047.5 (the remainder is 1, so 2 is not a divisor of 6095)
6095 / 3 = 2031.6666666667 (the remainder is 2, so 3 is not a divisor of 6095)
...
6095 / 77 = 79.155844155844 (the remainder is 12, so 77 is not a divisor of 6095)
6095 / 78 = 78.141025641026 (the remainder is 11, so 78 is not a divisor of 6095)