What are the divisors of 8116?

1, 2, 4, 2029, 4058, 8116

There is a total of 6 positive divisors.
The sum of these divisors is 14210.
The arithmetic mean is 2368.3333333333.

4 even divisors

2, 4, 4058, 8116

2 odd divisors

1, 2029

How to compute the divisors of 8116?

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 8116 by each of the numbers from 1 to 8116 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)

8116 / 1 = 8116 (the remainder is 0, so 1 is a divisor of 8116)
8116 / 2 = 4058 (the remainder is 0, so 2 is a divisor of 8116)
8116 / 3 = 2705.3333333333 (the remainder is 1, so 3 is not a divisor of 8116)
...
8116 / 8115 = 1.000123228589 (the remainder is 1, so 8115 is not a divisor of 8116)
8116 / 8116 = 1 (the remainder is 0, so 8116 is a divisor of 8116)

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 8116 (i.e. 90.088845036442). 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 $\frac{N}{d} = D$ )

8116 / 1 = 8116 (the remainder is 0, so 1 and 8116 are divisors of 8116)
8116 / 2 = 4058 (the remainder is 0, so 2 and 4058 are divisors of 8116)
8116 / 3 = 2705.3333333333 (the remainder is 1, so 3 is not a divisor of 8116)
...
8116 / 89 = 91.191011235955 (the remainder is 17, so 89 is not a divisor of 8116)
8116 / 90 = 90.177777777778 (the remainder is 16, so 90 is not a divisor of 8116)