What are the divisors of 8106?

1, 2, 3, 6, 7, 14, 21, 42, 193, 386, 579, 1158, 1351, 2702, 4053, 8106

There is a total of 16 positive divisors.
The sum of these divisors is 18624.
The arithmetic mean is 1164.

8 even divisors

2, 6, 14, 42, 386, 1158, 2702, 8106

8 odd divisors

1, 3, 7, 21, 193, 579, 1351, 4053

How to compute the divisors of 8106?

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 8106 by each of the numbers from 1 to 8106 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)

8106 / 1 = 8106 (the remainder is 0, so 1 is a divisor of 8106)
8106 / 2 = 4053 (the remainder is 0, so 2 is a divisor of 8106)
8106 / 3 = 2702 (the remainder is 0, so 3 is a divisor of 8106)
...
8106 / 8105 = 1.0001233806292 (the remainder is 1, so 8105 is not a divisor of 8106)
8106 / 8106 = 1 (the remainder is 0, so 8106 is a divisor of 8106)

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 8106 (i.e. 90.033327162779). 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 $\frac{N}{d} = D$ )

8106 / 1 = 8106 (the remainder is 0, so 1 and 8106 are divisors of 8106)
8106 / 2 = 4053 (the remainder is 0, so 2 and 4053 are divisors of 8106)
8106 / 3 = 2702 (the remainder is 0, so 3 and 2702 are divisors of 8106)
...
8106 / 89 = 91.078651685393 (the remainder is 7, so 89 is not a divisor of 8106)
8106 / 90 = 90.066666666667 (the remainder is 6, so 90 is not a divisor of 8106)