What are the divisors of 8082?

1, 2, 3, 6, 9, 18, 449, 898, 1347, 2694, 4041, 8082

There is a total of 12 positive divisors.
The sum of these divisors is 17550.
The arithmetic mean is 1462.5.

6 even divisors

2, 6, 18, 898, 2694, 8082

6 odd divisors

1, 3, 9, 449, 1347, 4041

How to compute the divisors of 8082?

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 8082 by each of the numbers from 1 to 8082 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)

8082 / 1 = 8082 (the remainder is 0, so 1 is a divisor of 8082)
8082 / 2 = 4041 (the remainder is 0, so 2 is a divisor of 8082)
8082 / 3 = 2694 (the remainder is 0, so 3 is a divisor of 8082)
...
8082 / 8081 = 1.000123747061 (the remainder is 1, so 8081 is not a divisor of 8082)
8082 / 8082 = 1 (the remainder is 0, so 8082 is a divisor of 8082)

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 8082 (i.e. 89.89994438263). 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 $\frac{N}{d} = D$ )

8082 / 1 = 8082 (the remainder is 0, so 1 and 8082 are divisors of 8082)
8082 / 2 = 4041 (the remainder is 0, so 2 and 4041 are divisors of 8082)
8082 / 3 = 2694 (the remainder is 0, so 3 and 2694 are divisors of 8082)
...
8082 / 88 = 91.840909090909 (the remainder is 74, so 88 is not a divisor of 8082)
8082 / 89 = 90.808988764045 (the remainder is 72, so 89 is not a divisor of 8082)