Prime factorization of $$$3609$$$

Find the prime factorization of $$$3609$$$.

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

Determine whether $$$3609$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3609$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3609$$$ by $$${\color{green}3}$$$: $$$\frac{3609}{3} = {\color{red}1203}$$$.

Determine whether $$$1203$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1203$$$ by $$${\color{green}3}$$$: $$$\frac{1203}{3} = {\color{red}401}$$$.

The prime number $$${\color{green}401}$$$ has no other factors then $$$1$$$ and $$${\color{green}401}$$$: $$$\frac{401}{401} = {\color{red}1}$$$.

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: $$$3609 = 3^{2} \cdot 401$$$.

The prime factorization is $$$3609 = 3^{2} \cdot 401$$$A.