What are the divisors of 6106?

1, 2, 43, 71, 86, 142, 3053, 6106

There is a total of 8 positive divisors.
The sum of these divisors is 9504.
The arithmetic mean is 1188.

4 even divisors

2, 86, 142, 6106

4 odd divisors

1, 43, 71, 3053

How to compute the divisors of 6106?

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 6106 by each of the numbers from 1 to 6106 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)

6106 / 1 = 6106 (the remainder is 0, so 1 is a divisor of 6106)
6106 / 2 = 3053 (the remainder is 0, so 2 is a divisor of 6106)
6106 / 3 = 2035.3333333333 (the remainder is 1, so 3 is not a divisor of 6106)
...
6106 / 6105 = 1.0001638001638 (the remainder is 1, so 6105 is not a divisor of 6106)
6106 / 6106 = 1 (the remainder is 0, so 6106 is a divisor of 6106)

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 6106 (i.e. 78.140898382345). 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 $\frac{N}{d} = D$ )

6106 / 1 = 6106 (the remainder is 0, so 1 and 6106 are divisors of 6106)
6106 / 2 = 3053 (the remainder is 0, so 2 and 3053 are divisors of 6106)
6106 / 3 = 2035.3333333333 (the remainder is 1, so 3 is not a divisor of 6106)
...
6106 / 77 = 79.298701298701 (the remainder is 23, so 77 is not a divisor of 6106)
6106 / 78 = 78.282051282051 (the remainder is 22, so 78 is not a divisor of 6106)