Prime factorization of $$$2228$$$

Find the prime factorization of $$$2228$$$.

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

Determine whether $$$2228$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2228$$$ by $$${\color{green}2}$$$: $$$\frac{2228}{2} = {\color{red}1114}$$$.

Determine whether $$$1114$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1114$$$ by $$${\color{green}2}$$$: $$$\frac{1114}{2} = {\color{red}557}$$$.

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: $$$2228 = 2^{2} \cdot 557$$$.

The prime factorization is $$$2228 = 2^{2} \cdot 557$$$A.