Prime factorization of $$$128$$$

Find the prime factorization of $$$128$$$.

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

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: $$$128 = 2^{7}$$$.

The prime factorization is $$$128 = 2^{7}$$$A.