# Prime factorization of $3789$

The calculator will find the prime factorization of $3789$, with steps shown.

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Find the prime factorization of $3789$.

### Solution

Start with the number $2$.

Determine whether $3789$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $3789$ is divisible by $3$.

It is divisible, thus, divide $3789$ by ${\color{green}3}$: $\frac{3789}{3} = {\color{red}1263}$.

Determine whether $1263$ is divisible by $3$.

It is divisible, thus, divide $1263$ by ${\color{green}3}$: $\frac{1263}{3} = {\color{red}421}$.

The prime number ${\color{green}421}$ has no other factors then $1$ and ${\color{green}421}$: $\frac{421}{421} = {\color{red}1}$.

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: $3789 = 3^{2} \cdot 421$.

The prime factorization is $3789 = 3^{2} \cdot 421$A.