What are the divisors of 8085?

1, 3, 5, 7, 11, 15, 21, 33, 35, 49, 55, 77, 105, 147, 165, 231, 245, 385, 539, 735, 1155, 1617, 2695, 8085

There is a total of 24 positive divisors.
The sum of these divisors is 16416.
The arithmetic mean is 684.

24 odd divisors

1, 3, 5, 7, 11, 15, 21, 33, 35, 49, 55, 77, 105, 147, 165, 231, 245, 385, 539, 735, 1155, 1617, 2695, 8085

How to compute the divisors of 8085?

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 8085 by each of the numbers from 1 to 8085 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)

8085 / 1 = 8085 (the remainder is 0, so 1 is a divisor of 8085)
8085 / 2 = 4042.5 (the remainder is 1, so 2 is not a divisor of 8085)
8085 / 3 = 2695 (the remainder is 0, so 3 is a divisor of 8085)
...
8085 / 8084 = 1.0001237011381 (the remainder is 1, so 8084 is not a divisor of 8085)
8085 / 8085 = 1 (the remainder is 0, so 8085 is a divisor of 8085)

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 8085 (i.e. 89.916628050656). 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 $\frac{N}{d} = D$ )

8085 / 1 = 8085 (the remainder is 0, so 1 and 8085 are divisors of 8085)
8085 / 2 = 4042.5 (the remainder is 1, so 2 is not a divisor of 8085)
8085 / 3 = 2695 (the remainder is 0, so 3 and 2695 are divisors of 8085)
...
8085 / 88 = 91.875 (the remainder is 77, so 88 is not a divisor of 8085)
8085 / 89 = 90.842696629213 (the remainder is 75, so 89 is not a divisor of 8085)