Prime factorization of $$$3789$$$

Find the prime factorization of $$$3789$$$.

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.