# Prime factorization of $387$

The calculator will find the prime factorization of $387$, with steps shown.

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Find the prime factorization of $387$.

### Solution

Start with the number $2$.

Determine whether $387$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $387$ is divisible by $3$.

It is divisible, thus, divide $387$ by ${\color{green}3}$: $\frac{387}{3} = {\color{red}129}$.

Determine whether $129$ is divisible by $3$.

It is divisible, thus, divide $129$ by ${\color{green}3}$: $\frac{129}{3} = {\color{red}43}$.

The prime number ${\color{green}43}$ has no other factors then $1$ and ${\color{green}43}$: $\frac{43}{43} = {\color{red}1}$.

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: $387 = 3^{2} \cdot 43$.

The prime factorization is $387 = 3^{2} \cdot 43$A.