What are the divisors of 8133?

1, 3, 2711, 8133

There is a total of 4 positive divisors.
The sum of these divisors is 10848.
The arithmetic mean is 2712.

4 odd divisors

1, 3, 2711, 8133

How to compute the divisors of 8133?

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 8133 by each of the numbers from 1 to 8133 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)

8133 / 1 = 8133 (the remainder is 0, so 1 is a divisor of 8133)
8133 / 2 = 4066.5 (the remainder is 1, so 2 is not a divisor of 8133)
8133 / 3 = 2711 (the remainder is 0, so 3 is a divisor of 8133)
...
8133 / 8132 = 1.0001229709788 (the remainder is 1, so 8132 is not a divisor of 8133)
8133 / 8133 = 1 (the remainder is 0, so 8133 is a divisor of 8133)

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 8133 (i.e. 90.183146984345). 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 $\frac{N}{d} = D$ )

8133 / 1 = 8133 (the remainder is 0, so 1 and 8133 are divisors of 8133)
8133 / 2 = 4066.5 (the remainder is 1, so 2 is not a divisor of 8133)
8133 / 3 = 2711 (the remainder is 0, so 3 and 2711 are divisors of 8133)
...
8133 / 89 = 91.38202247191 (the remainder is 34, so 89 is not a divisor of 8133)
8133 / 90 = 90.366666666667 (the remainder is 33, so 90 is not a divisor of 8133)