What are the divisors of 3166?

1, 2, 1583, 3166

There is a total of 4 positive divisors.
The sum of these divisors is 4752.
The arithmetic mean is 1188.

2 even divisors

2, 3166

2 odd divisors

1, 1583

How to compute the divisors of 3166?

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 3166 by each of the numbers from 1 to 3166 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)

3166 / 1 = 3166 (the remainder is 0, so 1 is a divisor of 3166)
3166 / 2 = 1583 (the remainder is 0, so 2 is a divisor of 3166)
3166 / 3 = 1055.3333333333 (the remainder is 1, so 3 is not a divisor of 3166)
...
3166 / 3165 = 1.0003159557662 (the remainder is 1, so 3165 is not a divisor of 3166)
3166 / 3166 = 1 (the remainder is 0, so 3166 is a divisor of 3166)

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 3166 (i.e. 56.267219586541). 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 $\frac{N}{d} = D$ )

3166 / 1 = 3166 (the remainder is 0, so 1 and 3166 are divisors of 3166)
3166 / 2 = 1583 (the remainder is 0, so 2 and 1583 are divisors of 3166)
3166 / 3 = 1055.3333333333 (the remainder is 1, so 3 is not a divisor of 3166)
...
3166 / 55 = 57.563636363636 (the remainder is 31, so 55 is not a divisor of 3166)
3166 / 56 = 56.535714285714 (the remainder is 30, so 56 is not a divisor of 3166)