# Prime factorization of $3900$

The calculator will find the prime factorization of $3900$, 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 $3900$.

### Solution

Start with the number $2$.

Determine whether $3900$ is divisible by $2$.

It is divisible, thus, divide $3900$ by ${\color{green}2}$: $\frac{3900}{2} = {\color{red}1950}$.

Determine whether $1950$ is divisible by $2$.

It is divisible, thus, divide $1950$ by ${\color{green}2}$: $\frac{1950}{2} = {\color{red}975}$.

Determine whether $975$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $975$ is divisible by $3$.

It is divisible, thus, divide $975$ by ${\color{green}3}$: $\frac{975}{3} = {\color{red}325}$.

Determine whether $325$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $325$ is divisible by $5$.

It is divisible, thus, divide $325$ by ${\color{green}5}$: $\frac{325}{5} = {\color{red}65}$.

Determine whether $65$ is divisible by $5$.

It is divisible, thus, divide $65$ by ${\color{green}5}$: $\frac{65}{5} = {\color{red}13}$.

The prime number ${\color{green}13}$ has no other factors then $1$ and ${\color{green}13}$: $\frac{13}{13} = {\color{red}1}$.

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: $3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13$.

The prime factorization is $3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13$A.