What are the divisors of 2066?

1, 2, 1033, 2066

There is a total of 4 positive divisors.
The sum of these divisors is 3102.
The arithmetic mean is 775.5.

2 even divisors

2, 2066

2 odd divisors

1, 1033

How to compute the divisors of 2066?

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 2066 by each of the numbers from 1 to 2066 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)

2066 / 1 = 2066 (the remainder is 0, so 1 is a divisor of 2066)
2066 / 2 = 1033 (the remainder is 0, so 2 is a divisor of 2066)
2066 / 3 = 688.66666666667 (the remainder is 2, so 3 is not a divisor of 2066)
...
2066 / 2065 = 1.0004842615012 (the remainder is 1, so 2065 is not a divisor of 2066)
2066 / 2066 = 1 (the remainder is 0, so 2066 is a divisor of 2066)

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 2066 (i.e. 45.453272709454). 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 $\frac{N}{d} = D$ )

2066 / 1 = 2066 (the remainder is 0, so 1 and 2066 are divisors of 2066)
2066 / 2 = 1033 (the remainder is 0, so 2 and 1033 are divisors of 2066)
2066 / 3 = 688.66666666667 (the remainder is 2, so 3 is not a divisor of 2066)
...
2066 / 44 = 46.954545454545 (the remainder is 42, so 44 is not a divisor of 2066)
2066 / 45 = 45.911111111111 (the remainder is 41, so 45 is not a divisor of 2066)