# Prime factorization of $3663$

The calculator will find the prime factorization of $3663$, with steps shown.

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Find the prime factorization of $3663$.

### Solution

Start with the number $2$.

Determine whether $3663$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3663$ is divisible by $3$.

It is divisible, thus, divide $3663$ by ${\color{green}3}$: $\frac{3663}{3} = {\color{red}1221}$.

Determine whether $1221$ is divisible by $3$.

It is divisible, thus, divide $1221$ by ${\color{green}3}$: $\frac{1221}{3} = {\color{red}407}$.

Determine whether $407$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $407$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $407$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $407$ is divisible by $11$.

It is divisible, thus, divide $407$ by ${\color{green}11}$: $\frac{407}{11} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $3663 = 3^{2} \cdot 11 \cdot 37$.

The prime factorization is $3663 = 3^{2} \cdot 11 \cdot 37$A.