What are the divisors of 8182?

1, 2, 4091, 8182

There is a total of 4 positive divisors.
The sum of these divisors is 12276.
The arithmetic mean is 3069.

2 even divisors

2, 8182

2 odd divisors

1, 4091

How to compute the divisors of 8182?

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 8182 by each of the numbers from 1 to 8182 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)

8182 / 1 = 8182 (the remainder is 0, so 1 is a divisor of 8182)
8182 / 2 = 4091 (the remainder is 0, so 2 is a divisor of 8182)
8182 / 3 = 2727.3333333333 (the remainder is 1, so 3 is not a divisor of 8182)
...
8182 / 8181 = 1.0001222344457 (the remainder is 1, so 8181 is not a divisor of 8182)
8182 / 8182 = 1 (the remainder is 0, so 8182 is a divisor of 8182)

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 8182 (i.e. 90.454408405561). 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 $\frac{N}{d} = D$ )

8182 / 1 = 8182 (the remainder is 0, so 1 and 8182 are divisors of 8182)
8182 / 2 = 4091 (the remainder is 0, so 2 and 4091 are divisors of 8182)
8182 / 3 = 2727.3333333333 (the remainder is 1, so 3 is not a divisor of 8182)
...
8182 / 89 = 91.932584269663 (the remainder is 83, so 89 is not a divisor of 8182)
8182 / 90 = 90.911111111111 (the remainder is 82, so 90 is not a divisor of 8182)