Prime factorization of $$$352$$$

Find the prime factorization of $$$352$$$.

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

Determine whether $$$352$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$352$$$ by $$${\color{green}2}$$$: $$$\frac{352}{2} = {\color{red}176}$$$.

Determine whether $$$176$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$176$$$ by $$${\color{green}2}$$$: $$$\frac{176}{2} = {\color{red}88}$$$.

Determine whether $$$88$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$88$$$ by $$${\color{green}2}$$$: $$$\frac{88}{2} = {\color{red}44}$$$.

Determine whether $$$44$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$44$$$ by $$${\color{green}2}$$$: $$$\frac{44}{2} = {\color{red}22}$$$.

Determine whether $$$22$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$22$$$ by $$${\color{green}2}$$$: $$$\frac{22}{2} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$352 = 2^{5} \cdot 11$$$.

The prime factorization is $$$352 = 2^{5} \cdot 11$$$A.