Prime factorization of $$$1197$$$

Find the prime factorization of $$$1197$$$.

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

Determine whether $$$1197$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1197$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1197$$$ by $$${\color{green}3}$$$: $$$\frac{1197}{3} = {\color{red}399}$$$.

Determine whether $$$399$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$399$$$ by $$${\color{green}3}$$$: $$$\frac{399}{3} = {\color{red}133}$$$.

Determine whether $$$133$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$133$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$133$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$133$$$ by $$${\color{green}7}$$$: $$$\frac{133}{7} = {\color{red}19}$$$.

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: $$$1197 = 3^{2} \cdot 7 \cdot 19$$$.

The prime factorization is $$$1197 = 3^{2} \cdot 7 \cdot 19$$$A.