What are the divisors of 8139?

1, 3, 2713, 8139

There is a total of 4 positive divisors.
The sum of these divisors is 10856.
The arithmetic mean is 2714.

4 odd divisors

1, 3, 2713, 8139

How to compute the divisors of 8139?

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 8139 by each of the numbers from 1 to 8139 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)

8139 / 1 = 8139 (the remainder is 0, so 1 is a divisor of 8139)
8139 / 2 = 4069.5 (the remainder is 1, so 2 is not a divisor of 8139)
8139 / 3 = 2713 (the remainder is 0, so 3 is a divisor of 8139)
...
8139 / 8138 = 1.0001228803146 (the remainder is 1, so 8138 is not a divisor of 8139)
8139 / 8139 = 1 (the remainder is 0, so 8139 is a divisor of 8139)

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 8139 (i.e. 90.216406490172). 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 $\frac{N}{d} = D$ )

8139 / 1 = 8139 (the remainder is 0, so 1 and 8139 are divisors of 8139)
8139 / 2 = 4069.5 (the remainder is 1, so 2 is not a divisor of 8139)
8139 / 3 = 2713 (the remainder is 0, so 3 and 2713 are divisors of 8139)
...
8139 / 89 = 91.449438202247 (the remainder is 40, so 89 is not a divisor of 8139)
8139 / 90 = 90.433333333333 (the remainder is 39, so 90 is not a divisor of 8139)