# Prime factorization of $$$114$$$

### Your Input

**Find the prime factorization of $$$114$$$.**

### Solution

Start with the number $$$2$$$.

Determine whether $$$114$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$114$$$ by $$${\color{green}2}$$$: $$$\frac{114}{2} = {\color{red}57}$$$.

Determine whether $$$57$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$57$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$57$$$ by $$${\color{green}3}$$$: $$$\frac{57}{3} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$114 = 2 \cdot 3 \cdot 19$$$.

### Answer

**The prime factorization is $$$114 = 2 \cdot 3 \cdot 19$$$A.**