Prime factorization of $$$336$$$

Find the prime factorization of $$$336$$$.

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

Determine whether $$$336$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$336$$$ by $$${\color{green}2}$$$: $$$\frac{336}{2} = {\color{red}168}$$$.

Determine whether $$$168$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$168$$$ by $$${\color{green}2}$$$: $$$\frac{168}{2} = {\color{red}84}$$$.

Determine whether $$$84$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$84$$$ by $$${\color{green}2}$$$: $$$\frac{84}{2} = {\color{red}42}$$$.

Determine whether $$$42$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$42$$$ by $$${\color{green}2}$$$: $$$\frac{42}{2} = {\color{red}21}$$$.

Determine whether $$$21$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$21$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$21$$$ by $$${\color{green}3}$$$: $$$\frac{21}{3} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$336 = 2^{4} \cdot 3 \cdot 7$$$.

The prime factorization is $$$336 = 2^{4} \cdot 3 \cdot 7$$$A.