# Prime factorization of $3200$

The calculator will find the prime factorization of $3200$, with steps shown.

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Find the prime factorization of $3200$.

### Solution

Start with the number $2$.

Determine whether $3200$ is divisible by $2$.

It is divisible, thus, divide $3200$ by ${\color{green}2}$: $\frac{3200}{2} = {\color{red}1600}$.

Determine whether $1600$ is divisible by $2$.

It is divisible, thus, divide $1600$ by ${\color{green}2}$: $\frac{1600}{2} = {\color{red}800}$.

Determine whether $800$ is divisible by $2$.

It is divisible, thus, divide $800$ by ${\color{green}2}$: $\frac{800}{2} = {\color{red}400}$.

Determine whether $400$ is divisible by $2$.

It is divisible, thus, divide $400$ by ${\color{green}2}$: $\frac{400}{2} = {\color{red}200}$.

Determine whether $200$ is divisible by $2$.

It is divisible, thus, divide $200$ by ${\color{green}2}$: $\frac{200}{2} = {\color{red}100}$.

Determine whether $100$ is divisible by $2$.

It is divisible, thus, divide $100$ by ${\color{green}2}$: $\frac{100}{2} = {\color{red}50}$.

Determine whether $50$ is divisible by $2$.

It is divisible, thus, divide $50$ by ${\color{green}2}$: $\frac{50}{2} = {\color{red}25}$.

Determine whether $25$ is divisible by $2$.

Since it is not divisible, move to the next prime number.

The next prime number is $3$.

Determine whether $25$ is divisible by $3$.

Since it is not divisible, move to the next prime number.

The next prime number is $5$.

Determine whether $25$ is divisible by $5$.

It is divisible, thus, divide $25$ by ${\color{green}5}$: $\frac{25}{5} = {\color{red}5}$.

The prime number ${\color{green}5}$ has no other factors then $1$ and ${\color{green}5}$: $\frac{5}{5} = {\color{red}1}$.

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: $3200 = 2^{7} \cdot 5^{2}$.

The prime factorization is $3200 = 2^{7} \cdot 5^{2}$A.