What are the divisors of 4086?

1, 2, 3, 6, 9, 18, 227, 454, 681, 1362, 2043, 4086

There is a total of 12 positive divisors.
The sum of these divisors is 8892.
The arithmetic mean is 741.

6 even divisors

2, 6, 18, 454, 1362, 4086

6 odd divisors

1, 3, 9, 227, 681, 2043

How to compute the divisors of 4086?

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 4086 by each of the numbers from 1 to 4086 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)

4086 / 1 = 4086 (the remainder is 0, so 1 is a divisor of 4086)
4086 / 2 = 2043 (the remainder is 0, so 2 is a divisor of 4086)
4086 / 3 = 1362 (the remainder is 0, so 3 is a divisor of 4086)
...
4086 / 4085 = 1.0002447980416 (the remainder is 1, so 4085 is not a divisor of 4086)
4086 / 4086 = 1 (the remainder is 0, so 4086 is a divisor of 4086)

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 4086 (i.e. 63.921827257988). 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 $\frac{N}{d} = D$ )

4086 / 1 = 4086 (the remainder is 0, so 1 and 4086 are divisors of 4086)
4086 / 2 = 2043 (the remainder is 0, so 2 and 2043 are divisors of 4086)
4086 / 3 = 1362 (the remainder is 0, so 3 and 1362 are divisors of 4086)
...
4086 / 62 = 65.903225806452 (the remainder is 56, so 62 is not a divisor of 4086)
4086 / 63 = 64.857142857143 (the remainder is 54, so 63 is not a divisor of 4086)