What are the divisors of 8168?

1, 2, 4, 8, 1021, 2042, 4084, 8168

There is a total of 8 positive divisors.
The sum of these divisors is 15330.
The arithmetic mean is 1916.25.

6 even divisors

2, 4, 8, 2042, 4084, 8168

2 odd divisors

1, 1021

How to compute the divisors of 8168?

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 8168 by each of the numbers from 1 to 8168 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)

8168 / 1 = 8168 (the remainder is 0, so 1 is a divisor of 8168)
8168 / 2 = 4084 (the remainder is 0, so 2 is a divisor of 8168)
8168 / 3 = 2722.6666666667 (the remainder is 2, so 3 is not a divisor of 8168)
...
8168 / 8167 = 1.0001224439819 (the remainder is 1, so 8167 is not a divisor of 8168)
8168 / 8168 = 1 (the remainder is 0, so 8168 is a divisor of 8168)

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 8168 (i.e. 90.37698822156). 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 $\frac{N}{d} = D$ )

8168 / 1 = 8168 (the remainder is 0, so 1 and 8168 are divisors of 8168)
8168 / 2 = 4084 (the remainder is 0, so 2 and 4084 are divisors of 8168)
8168 / 3 = 2722.6666666667 (the remainder is 2, so 3 is not a divisor of 8168)
...
8168 / 89 = 91.775280898876 (the remainder is 69, so 89 is not a divisor of 8168)
8168 / 90 = 90.755555555556 (the remainder is 68, so 90 is not a divisor of 8168)