Prime factorization of $$$171$$$

Find the prime factorization of $$$171$$$.

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

Determine whether $$$171$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$171$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$171$$$ by $$${\color{green}3}$$$: $$$\frac{171}{3} = {\color{red}57}$$$.

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: $$$171 = 3^{2} \cdot 19$$$.

The prime factorization is $$$171 = 3^{2} \cdot 19$$$A.