Prime factorization of $$$3606$$$

Find the prime factorization of $$$3606$$$.

Start with the number $$$2$$$.

Determine whether $$$3606$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3606$$$ by $$${\color{green}2}$$$: $$$\frac{3606}{2} = {\color{red}1803}$$$.

Determine whether $$$1803$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$1803$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1803$$$ by $$${\color{green}3}$$$: $$$\frac{1803}{3} = {\color{red}601}$$$.

The prime number $$${\color{green}601}$$$ has no other factors then $$$1$$$ and $$${\color{green}601}$$$: $$$\frac{601}{601} = {\color{red}1}$$$.

Since we have obtained $$$1$$$, we are done.

Now, just count the number of occurences of the divisors (green numbers), and write down the prime factorization: $$$3606 = 2 \cdot 3 \cdot 601$$$.

The prime factorization is $$$3606 = 2 \cdot 3 \cdot 601$$$A.