What are the divisors of 8084?

1, 2, 4, 43, 47, 86, 94, 172, 188, 2021, 4042, 8084

There is a total of 12 positive divisors.
The sum of these divisors is 14784.
The arithmetic mean is 1232.

8 even divisors

2, 4, 86, 94, 172, 188, 4042, 8084

4 odd divisors

1, 43, 47, 2021

How to compute the divisors of 8084?

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 8084 by each of the numbers from 1 to 8084 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)

8084 / 1 = 8084 (the remainder is 0, so 1 is a divisor of 8084)
8084 / 2 = 4042 (the remainder is 0, so 2 is a divisor of 8084)
8084 / 3 = 2694.6666666667 (the remainder is 2, so 3 is not a divisor of 8084)
...
8084 / 8083 = 1.0001237164419 (the remainder is 1, so 8083 is not a divisor of 8084)
8084 / 8084 = 1 (the remainder is 0, so 8084 is a divisor of 8084)

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 8084 (i.e. 89.911067171956). 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 $\frac{N}{d} = D$ )

8084 / 1 = 8084 (the remainder is 0, so 1 and 8084 are divisors of 8084)
8084 / 2 = 4042 (the remainder is 0, so 2 and 4042 are divisors of 8084)
8084 / 3 = 2694.6666666667 (the remainder is 2, so 3 is not a divisor of 8084)
...
8084 / 88 = 91.863636363636 (the remainder is 76, so 88 is not a divisor of 8084)
8084 / 89 = 90.831460674157 (the remainder is 74, so 89 is not a divisor of 8084)