Prime factorization of $$$352$$$
Your Input
Find the prime factorization of $$$352$$$.
Solution
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: $$$352 = 2^{5} \cdot 11$$$.
Answer
The prime factorization is $$$352 = 2^{5} \cdot 11$$$A.