What are the divisors of 8163?

1, 3, 9, 907, 2721, 8163

There is a total of 6 positive divisors.
The sum of these divisors is 11804.
The arithmetic mean is 1967.3333333333.

6 odd divisors

1, 3, 9, 907, 2721, 8163

How to compute the divisors of 8163?

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 8163 by each of the numbers from 1 to 8163 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)

8163 / 1 = 8163 (the remainder is 0, so 1 is a divisor of 8163)
8163 / 2 = 4081.5 (the remainder is 1, so 2 is not a divisor of 8163)
8163 / 3 = 2721 (the remainder is 0, so 3 is a divisor of 8163)
...
8163 / 8162 = 1.0001225189904 (the remainder is 1, so 8162 is not a divisor of 8163)
8163 / 8163 = 1 (the remainder is 0, so 8163 is a divisor of 8163)

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 8163 (i.e. 90.349322078254). 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 $\frac{N}{d} = D$ )

8163 / 1 = 8163 (the remainder is 0, so 1 and 8163 are divisors of 8163)
8163 / 2 = 4081.5 (the remainder is 1, so 2 is not a divisor of 8163)
8163 / 3 = 2721 (the remainder is 0, so 3 and 2721 are divisors of 8163)
...
8163 / 89 = 91.719101123596 (the remainder is 64, so 89 is not a divisor of 8163)
8163 / 90 = 90.7 (the remainder is 63, so 90 is not a divisor of 8163)