Prime factorization of $$$648$$$

Find the prime factorization of $$$648$$$.

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

Determine whether $$$648$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$648$$$ by $$${\color{green}2}$$$: $$$\frac{648}{2} = {\color{red}324}$$$.

Determine whether $$$324$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$324$$$ by $$${\color{green}2}$$$: $$$\frac{324}{2} = {\color{red}162}$$$.

Determine whether $$$162$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$162$$$ by $$${\color{green}2}$$$: $$$\frac{162}{2} = {\color{red}81}$$$.

Determine whether $$$81$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$81$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$81$$$ by $$${\color{green}3}$$$: $$$\frac{81}{3} = {\color{red}27}$$$.

Determine whether $$$27$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$27$$$ by $$${\color{green}3}$$$: $$$\frac{27}{3} = {\color{red}9}$$$.

Determine whether $$$9$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$9$$$ by $$${\color{green}3}$$$: $$$\frac{9}{3} = {\color{red}3}$$$.

The prime number $$${\color{green}3}$$$ has no other factors then $$$1$$$ and $$${\color{green}3}$$$: $$$\frac{3}{3} = {\color{red}1}$$$.

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: $$$648 = 2^{3} \cdot 3^{4}$$$.

The prime factorization is $$$648 = 2^{3} \cdot 3^{4}$$$A.