# Prime factorization of $352$

The calculator will find the prime factorization of $352$, with steps shown.

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

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