What are the divisors of 6066?

1, 2, 3, 6, 9, 18, 337, 674, 1011, 2022, 3033, 6066

There is a total of 12 positive divisors.
The sum of these divisors is 13182.
The arithmetic mean is 1098.5.

6 even divisors

2, 6, 18, 674, 2022, 6066

6 odd divisors

1, 3, 9, 337, 1011, 3033

How to compute the divisors of 6066?

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 6066 by each of the numbers from 1 to 6066 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)

6066 / 1 = 6066 (the remainder is 0, so 1 is a divisor of 6066)
6066 / 2 = 3033 (the remainder is 0, so 2 is a divisor of 6066)
6066 / 3 = 2022 (the remainder is 0, so 3 is a divisor of 6066)
...
6066 / 6065 = 1.0001648804617 (the remainder is 1, so 6065 is not a divisor of 6066)
6066 / 6066 = 1 (the remainder is 0, so 6066 is a divisor of 6066)

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 6066 (i.e. 77.884529914483). 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 $\frac{N}{d} = D$ )

6066 / 1 = 6066 (the remainder is 0, so 1 and 6066 are divisors of 6066)
6066 / 2 = 3033 (the remainder is 0, so 2 and 3033 are divisors of 6066)
6066 / 3 = 2022 (the remainder is 0, so 3 and 2022 are divisors of 6066)
...
6066 / 76 = 79.815789473684 (the remainder is 62, so 76 is not a divisor of 6066)
6066 / 77 = 78.779220779221 (the remainder is 60, so 77 is not a divisor of 6066)