# Prime factorization of $$$3900$$$

### Your Input

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

### Answer

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