Prime factorization of $$$3342$$$

Find the prime factorization of $$$3342$$$.

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

Determine whether $$$3342$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3342$$$ by $$${\color{green}2}$$$: $$$\frac{3342}{2} = {\color{red}1671}$$$.

Determine whether $$$1671$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1671$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1671$$$ by $$${\color{green}3}$$$: $$$\frac{1671}{3} = {\color{red}557}$$$.

The prime number $$${\color{green}557}$$$ has no other factors then $$$1$$$ and $$${\color{green}557}$$$: $$$\frac{557}{557} = {\color{red}1}$$$.

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: $$$3342 = 2 \cdot 3 \cdot 557$$$.

The prime factorization is $$$3342 = 2 \cdot 3 \cdot 557$$$A.