What are the divisors of 4066?

1, 2, 19, 38, 107, 214, 2033, 4066

There is a total of 8 positive divisors.
The sum of these divisors is 6480.
The arithmetic mean is 810.

4 even divisors

2, 38, 214, 4066

4 odd divisors

1, 19, 107, 2033

How to compute the divisors of 4066?

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 4066 by each of the numbers from 1 to 4066 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)

4066 / 1 = 4066 (the remainder is 0, so 1 is a divisor of 4066)
4066 / 2 = 2033 (the remainder is 0, so 2 is a divisor of 4066)
4066 / 3 = 1355.3333333333 (the remainder is 1, so 3 is not a divisor of 4066)
...
4066 / 4065 = 1.00024600246 (the remainder is 1, so 4065 is not a divisor of 4066)
4066 / 4066 = 1 (the remainder is 0, so 4066 is a divisor of 4066)

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 4066 (i.e. 63.765194267719). 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 $\frac{N}{d} = D$ )

4066 / 1 = 4066 (the remainder is 0, so 1 and 4066 are divisors of 4066)
4066 / 2 = 2033 (the remainder is 0, so 2 and 2033 are divisors of 4066)
4066 / 3 = 1355.3333333333 (the remainder is 1, so 3 is not a divisor of 4066)
...
4066 / 62 = 65.58064516129 (the remainder is 36, so 62 is not a divisor of 4066)
4066 / 63 = 64.539682539683 (the remainder is 34, so 63 is not a divisor of 4066)