# Prime factorization of $3152$

The calculator will find the prime factorization of $3152$, with steps shown.

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Find the prime factorization of $3152$.

### Solution

Start with the number $2$.

Determine whether $3152$ is divisible by $2$.

It is divisible, thus, divide $3152$ by ${\color{green}2}$: $\frac{3152}{2} = {\color{red}1576}$.

Determine whether $1576$ is divisible by $2$.

It is divisible, thus, divide $1576$ by ${\color{green}2}$: $\frac{1576}{2} = {\color{red}788}$.

Determine whether $788$ is divisible by $2$.

It is divisible, thus, divide $788$ by ${\color{green}2}$: $\frac{788}{2} = {\color{red}394}$.

Determine whether $394$ is divisible by $2$.

It is divisible, thus, divide $394$ by ${\color{green}2}$: $\frac{394}{2} = {\color{red}197}$.

The prime number ${\color{green}197}$ has no other factors then $1$ and ${\color{green}197}$: $\frac{197}{197} = {\color{red}1}$.

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: $3152 = 2^{4} \cdot 197$.

The prime factorization is $3152 = 2^{4} \cdot 197$A.