What are the divisors of 6166?

1, 2, 3083, 6166

There is a total of 4 positive divisors.
The sum of these divisors is 9252.
The arithmetic mean is 2313.

2 even divisors

2, 6166

2 odd divisors

1, 3083

How to compute the divisors of 6166?

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 6166 by each of the numbers from 1 to 6166 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)

6166 / 1 = 6166 (the remainder is 0, so 1 is a divisor of 6166)
6166 / 2 = 3083 (the remainder is 0, so 2 is a divisor of 6166)
6166 / 3 = 2055.3333333333 (the remainder is 1, so 3 is not a divisor of 6166)
...
6166 / 6165 = 1.0001622060016 (the remainder is 1, so 6165 is not a divisor of 6166)
6166 / 6166 = 1 (the remainder is 0, so 6166 is a divisor of 6166)

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 6166 (i.e. 78.523881717602). 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 $\frac{N}{d} = D$ )

6166 / 1 = 6166 (the remainder is 0, so 1 and 6166 are divisors of 6166)
6166 / 2 = 3083 (the remainder is 0, so 2 and 3083 are divisors of 6166)
6166 / 3 = 2055.3333333333 (the remainder is 1, so 3 is not a divisor of 6166)
...
6166 / 77 = 80.077922077922 (the remainder is 6, so 77 is not a divisor of 6166)
6166 / 78 = 79.051282051282 (the remainder is 4, so 78 is not a divisor of 6166)