What are the divisors of 8095?

1, 5, 1619, 8095

There is a total of 4 positive divisors.
The sum of these divisors is 9720.
The arithmetic mean is 2430.

4 odd divisors

1, 5, 1619, 8095

How to compute the divisors of 8095?

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 8095 by each of the numbers from 1 to 8095 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)

8095 / 1 = 8095 (the remainder is 0, so 1 is a divisor of 8095)
8095 / 2 = 4047.5 (the remainder is 1, so 2 is not a divisor of 8095)
8095 / 3 = 2698.3333333333 (the remainder is 1, so 3 is not a divisor of 8095)
...
8095 / 8094 = 1.0001235483074 (the remainder is 1, so 8094 is not a divisor of 8095)
8095 / 8095 = 1 (the remainder is 0, so 8095 is a divisor of 8095)

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 8095 (i.e. 89.972217934205). 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 $\frac{N}{d} = D$ )

8095 / 1 = 8095 (the remainder is 0, so 1 and 8095 are divisors of 8095)
8095 / 2 = 4047.5 (the remainder is 1, so 2 is not a divisor of 8095)
8095 / 3 = 2698.3333333333 (the remainder is 1, so 3 is not a divisor of 8095)
...
8095 / 88 = 91.988636363636 (the remainder is 87, so 88 is not a divisor of 8095)
8095 / 89 = 90.955056179775 (the remainder is 85, so 89 is not a divisor of 8095)