# Prime factorization of $66$

The calculator will find the prime factorization of $66$, with steps shown.

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Find the prime factorization of $66$.

### Solution

Start with the number $2$.

Determine whether $66$ is divisible by $2$.

It is divisible, thus, divide $66$ by ${\color{green}2}$: $\frac{66}{2} = {\color{red}33}$.

Determine whether $33$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $33$ is divisible by $3$.

It is divisible, thus, divide $33$ by ${\color{green}3}$: $\frac{33}{3} = {\color{red}11}$.

The prime number ${\color{green}11}$ has no other factors then $1$ and ${\color{green}11}$: $\frac{11}{11} = {\color{red}1}$.

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: $66 = 2 \cdot 3 \cdot 11$.

The prime factorization is $66 = 2 \cdot 3 \cdot 11$A.