# Prime factorization of $1206$

The calculator will find the prime factorization of $1206$, with steps shown.

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Find the prime factorization of $1206$.

### Solution

Start with the number $2$.

Determine whether $1206$ is divisible by $2$.

It is divisible, thus, divide $1206$ by ${\color{green}2}$: $\frac{1206}{2} = {\color{red}603}$.

Determine whether $603$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $603$ is divisible by $3$.

It is divisible, thus, divide $603$ by ${\color{green}3}$: $\frac{603}{3} = {\color{red}201}$.

Determine whether $201$ is divisible by $3$.

It is divisible, thus, divide $201$ by ${\color{green}3}$: $\frac{201}{3} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $1206 = 2 \cdot 3^{2} \cdot 67$.

The prime factorization is $1206 = 2 \cdot 3^{2} \cdot 67$A.