Prime factorization of $$$3378$$$

Find the prime factorization of $$$3378$$$.

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

Determine whether $$$3378$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3378$$$ by $$${\color{green}2}$$$: $$$\frac{3378}{2} = {\color{red}1689}$$$.

Determine whether $$$1689$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1689$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1689$$$ by $$${\color{green}3}$$$: $$$\frac{1689}{3} = {\color{red}563}$$$.

The prime number $$${\color{green}563}$$$ has no other factors then $$$1$$$ and $$${\color{green}563}$$$: $$$\frac{563}{563} = {\color{red}1}$$$.

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: $$$3378 = 2 \cdot 3 \cdot 563$$$.

The prime factorization is $$$3378 = 2 \cdot 3 \cdot 563$$$A.