# Prime factorization of $1989$

The calculator will find the prime factorization of $1989$, with steps shown.

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Find the prime factorization of $1989$.

### Solution

Start with the number $2$.

Determine whether $1989$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1989$ is divisible by $3$.

It is divisible, thus, divide $1989$ by ${\color{green}3}$: $\frac{1989}{3} = {\color{red}663}$.

Determine whether $663$ is divisible by $3$.

It is divisible, thus, divide $663$ by ${\color{green}3}$: $\frac{663}{3} = {\color{red}221}$.

Determine whether $221$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $221$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $221$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $221$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $221$ is divisible by $13$.

It is divisible, thus, divide $221$ by ${\color{green}13}$: $\frac{221}{13} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $1989 = 3^{2} \cdot 13 \cdot 17$.

The prime factorization is $1989 = 3^{2} \cdot 13 \cdot 17$A.