What are the divisors of 8206?

1, 2, 11, 22, 373, 746, 4103, 8206

There is a total of 8 positive divisors.
The sum of these divisors is 13464.
The arithmetic mean is 1683.

4 even divisors

2, 22, 746, 8206

4 odd divisors

1, 11, 373, 4103

How to compute the divisors of 8206?

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 8206 by each of the numbers from 1 to 8206 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)

8206 / 1 = 8206 (the remainder is 0, so 1 is a divisor of 8206)
8206 / 2 = 4103 (the remainder is 0, so 2 is a divisor of 8206)
8206 / 3 = 2735.3333333333 (the remainder is 1, so 3 is not a divisor of 8206)
...
8206 / 8205 = 1.0001218769043 (the remainder is 1, so 8205 is not a divisor of 8206)
8206 / 8206 = 1 (the remainder is 0, so 8206 is a divisor of 8206)

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 8206 (i.e. 90.586974781146). 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 $\frac{N}{d} = D$ )

8206 / 1 = 8206 (the remainder is 0, so 1 and 8206 are divisors of 8206)
8206 / 2 = 4103 (the remainder is 0, so 2 and 4103 are divisors of 8206)
8206 / 3 = 2735.3333333333 (the remainder is 1, so 3 is not a divisor of 8206)
...
8206 / 89 = 92.202247191011 (the remainder is 18, so 89 is not a divisor of 8206)
8206 / 90 = 91.177777777778 (the remainder is 16, so 90 is not a divisor of 8206)