Prime factorization of $$$4096$$$

Find the prime factorization of $$$4096$$$.

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

Determine whether $$$4096$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4096$$$ by $$${\color{green}2}$$$: $$$\frac{4096}{2} = {\color{red}2048}$$$.

Determine whether $$$2048$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2048$$$ by $$${\color{green}2}$$$: $$$\frac{2048}{2} = {\color{red}1024}$$$.

Determine whether $$$1024$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1024$$$ by $$${\color{green}2}$$$: $$$\frac{1024}{2} = {\color{red}512}$$$.

Determine whether $$$512$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$512$$$ by $$${\color{green}2}$$$: $$$\frac{512}{2} = {\color{red}256}$$$.

Determine whether $$$256$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$256$$$ by $$${\color{green}2}$$$: $$$\frac{256}{2} = {\color{red}128}$$$.

Determine whether $$$128$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$128$$$ by $$${\color{green}2}$$$: $$$\frac{128}{2} = {\color{red}64}$$$.

Determine whether $$$64$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$64$$$ by $$${\color{green}2}$$$: $$$\frac{64}{2} = {\color{red}32}$$$.

Determine whether $$$32$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$32$$$ by $$${\color{green}2}$$$: $$$\frac{32}{2} = {\color{red}16}$$$.

Determine whether $$$16$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$16$$$ by $$${\color{green}2}$$$: $$$\frac{16}{2} = {\color{red}8}$$$.

Determine whether $$$8$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$8$$$ by $$${\color{green}2}$$$: $$$\frac{8}{2} = {\color{red}4}$$$.

Determine whether $$$4$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4$$$ by $$${\color{green}2}$$$: $$$\frac{4}{2} = {\color{red}2}$$$.

The prime number $$${\color{green}2}$$$ has no other factors then $$$1$$$ and $$${\color{green}2}$$$: $$$\frac{2}{2} = {\color{red}1}$$$.

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: $$$4096 = 2^{12}$$$.

The prime factorization is $$$4096 = 2^{12}$$$A.