# Prime factorization of $1200$

The calculator will find the prime factorization of $1200$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $1200$.

### Solution

Start with the number $2$.

Determine whether $1200$ is divisible by $2$.

It is divisible, thus, divide $1200$ by ${\color{green}2}$: $\frac{1200}{2} = {\color{red}600}$.

Determine whether $600$ is divisible by $2$.

It is divisible, thus, divide $600$ by ${\color{green}2}$: $\frac{600}{2} = {\color{red}300}$.

Determine whether $300$ is divisible by $2$.

It is divisible, thus, divide $300$ by ${\color{green}2}$: $\frac{300}{2} = {\color{red}150}$.

Determine whether $150$ is divisible by $2$.

It is divisible, thus, divide $150$ by ${\color{green}2}$: $\frac{150}{2} = {\color{red}75}$.

Determine whether $75$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $75$ is divisible by $3$.

It is divisible, thus, divide $75$ by ${\color{green}3}$: $\frac{75}{3} = {\color{red}25}$.

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: $1200 = 2^{4} \cdot 3 \cdot 5^{2}$.

The prime factorization is $1200 = 2^{4} \cdot 3 \cdot 5^{2}$A.