Prime factorization of $$$2144$$$

Find the prime factorization of $$$2144$$$.

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

Determine whether $$$2144$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2144$$$ by $$${\color{green}2}$$$: $$$\frac{2144}{2} = {\color{red}1072}$$$.

Determine whether $$$1072$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1072$$$ by $$${\color{green}2}$$$: $$$\frac{1072}{2} = {\color{red}536}$$$.

Determine whether $$$536$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$536$$$ by $$${\color{green}2}$$$: $$$\frac{536}{2} = {\color{red}268}$$$.

Determine whether $$$268$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$268$$$ by $$${\color{green}2}$$$: $$$\frac{268}{2} = {\color{red}134}$$$.

Determine whether $$$134$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$134$$$ by $$${\color{green}2}$$$: $$$\frac{134}{2} = {\color{red}67}$$$.

The prime number $$${\color{green}67}$$$ has no other factors then $$$1$$$ and $$${\color{green}67}$$$: $$$\frac{67}{67} = {\color{red}1}$$$.

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: $$$2144 = 2^{5} \cdot 67$$$.

The prime factorization is $$$2144 = 2^{5} \cdot 67$$$A.