# Prime factorization of $1197$

The calculator will find the prime factorization of $1197$, with steps shown.

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Find the prime factorization of $1197$.

### Solution

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.