Prime factorization of $$$3352$$$

Find the prime factorization of $$$3352$$$.

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

Determine whether $$$3352$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3352$$$ by $$${\color{green}2}$$$: $$$\frac{3352}{2} = {\color{red}1676}$$$.

Determine whether $$$1676$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1676$$$ by $$${\color{green}2}$$$: $$$\frac{1676}{2} = {\color{red}838}$$$.

Determine whether $$$838$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$838$$$ by $$${\color{green}2}$$$: $$$\frac{838}{2} = {\color{red}419}$$$.

The prime number $$${\color{green}419}$$$ has no other factors then $$$1$$$ and $$${\color{green}419}$$$: $$$\frac{419}{419} = {\color{red}1}$$$.

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: $$$3352 = 2^{3} \cdot 419$$$.

The prime factorization is $$$3352 = 2^{3} \cdot 419$$$A.