Prime factorization of $$$3798$$$

Find the prime factorization of $$$3798$$$.

Start with the number $$$2$$$.

Determine whether $$$3798$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3798$$$ by $$${\color{green}2}$$$: $$$\frac{3798}{2} = {\color{red}1899}$$$.

Determine whether $$$1899$$$ is divisible by $$$2$$$.

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

The next prime number is $$$3$$$.

Determine whether $$$1899$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1899$$$ by $$${\color{green}3}$$$: $$$\frac{1899}{3} = {\color{red}633}$$$.

Determine whether $$$633$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$633$$$ by $$${\color{green}3}$$$: $$$\frac{633}{3} = {\color{red}211}$$$.

The prime number $$${\color{green}211}$$$ has no other factors then $$$1$$$ and $$${\color{green}211}$$$: $$$\frac{211}{211} = {\color{red}1}$$$.

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: $$$3798 = 2 \cdot 3^{2} \cdot 211$$$.

The prime factorization is $$$3798 = 2 \cdot 3^{2} \cdot 211$$$A.