What are the divisors of 8199?

1, 3, 9, 911, 2733, 8199

There is a total of 6 positive divisors.
The sum of these divisors is 11856.
The arithmetic mean is 1976.

6 odd divisors

1, 3, 9, 911, 2733, 8199

How to compute the divisors of 8199?

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 8199 by each of the numbers from 1 to 8199 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)

8199 / 1 = 8199 (the remainder is 0, so 1 is a divisor of 8199)
8199 / 2 = 4099.5 (the remainder is 1, so 2 is not a divisor of 8199)
8199 / 3 = 2733 (the remainder is 0, so 3 is a divisor of 8199)
...
8199 / 8198 = 1.000121980971 (the remainder is 1, so 8198 is not a divisor of 8199)
8199 / 8199 = 1 (the remainder is 0, so 8199 is a divisor of 8199)

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 8199 (i.e. 90.548329636719). 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 $\frac{N}{d} = D$ )

8199 / 1 = 8199 (the remainder is 0, so 1 and 8199 are divisors of 8199)
8199 / 2 = 4099.5 (the remainder is 1, so 2 is not a divisor of 8199)
8199 / 3 = 2733 (the remainder is 0, so 3 and 2733 are divisors of 8199)
...
8199 / 89 = 92.123595505618 (the remainder is 11, so 89 is not a divisor of 8199)
8199 / 90 = 91.1 (the remainder is 9, so 90 is not a divisor of 8199)