What are the divisors of 8115?

1, 3, 5, 15, 541, 1623, 2705, 8115

There is a total of 8 positive divisors.
The sum of these divisors is 13008.
The arithmetic mean is 1626.

8 odd divisors

1, 3, 5, 15, 541, 1623, 2705, 8115

How to compute the divisors of 8115?

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 8115 by each of the numbers from 1 to 8115 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)

8115 / 1 = 8115 (the remainder is 0, so 1 is a divisor of 8115)
8115 / 2 = 4057.5 (the remainder is 1, so 2 is not a divisor of 8115)
8115 / 3 = 2705 (the remainder is 0, so 3 is a divisor of 8115)
...
8115 / 8114 = 1.0001232437762 (the remainder is 1, so 8114 is not a divisor of 8115)
8115 / 8115 = 1 (the remainder is 0, so 8115 is a divisor of 8115)

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 8115 (i.e. 90.083294788768). 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 $\frac{N}{d} = D$ )

8115 / 1 = 8115 (the remainder is 0, so 1 and 8115 are divisors of 8115)
8115 / 2 = 4057.5 (the remainder is 1, so 2 is not a divisor of 8115)
8115 / 3 = 2705 (the remainder is 0, so 3 and 2705 are divisors of 8115)
...
8115 / 89 = 91.179775280899 (the remainder is 16, so 89 is not a divisor of 8115)
8115 / 90 = 90.166666666667 (the remainder is 15, so 90 is not a divisor of 8115)