# Prime factorization of $336$

The calculator will find the prime factorization of $336$, with steps shown.

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Find the prime factorization of $336$.

### Solution

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.