Prime factorization of $$$2272$$$

Find the prime factorization of $$$2272$$$.

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

Determine whether $$$2272$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2272$$$ by $$${\color{green}2}$$$: $$$\frac{2272}{2} = {\color{red}1136}$$$.

Determine whether $$$1136$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1136$$$ by $$${\color{green}2}$$$: $$$\frac{1136}{2} = {\color{red}568}$$$.

Determine whether $$$568$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$568$$$ by $$${\color{green}2}$$$: $$$\frac{568}{2} = {\color{red}284}$$$.

Determine whether $$$284$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$284$$$ by $$${\color{green}2}$$$: $$$\frac{284}{2} = {\color{red}142}$$$.

Determine whether $$$142$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$142$$$ by $$${\color{green}2}$$$: $$$\frac{142}{2} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$2272 = 2^{5} \cdot 71$$$.

The prime factorization is $$$2272 = 2^{5} \cdot 71$$$A.