Prime factorization of $$$4864$$$

Find the prime factorization of $$$4864$$$.

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

Determine whether $$$4864$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4864$$$ by $$${\color{green}2}$$$: $$$\frac{4864}{2} = {\color{red}2432}$$$.

Determine whether $$$2432$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2432$$$ by $$${\color{green}2}$$$: $$$\frac{2432}{2} = {\color{red}1216}$$$.

Determine whether $$$1216$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1216$$$ by $$${\color{green}2}$$$: $$$\frac{1216}{2} = {\color{red}608}$$$.

Determine whether $$$608$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$608$$$ by $$${\color{green}2}$$$: $$$\frac{608}{2} = {\color{red}304}$$$.

Determine whether $$$304$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$304$$$ by $$${\color{green}2}$$$: $$$\frac{304}{2} = {\color{red}152}$$$.

Determine whether $$$152$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$152$$$ by $$${\color{green}2}$$$: $$$\frac{152}{2} = {\color{red}76}$$$.

Determine whether $$$76$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$76$$$ by $$${\color{green}2}$$$: $$$\frac{76}{2} = {\color{red}38}$$$.

Determine whether $$$38$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$38$$$ by $$${\color{green}2}$$$: $$$\frac{38}{2} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$4864 = 2^{8} \cdot 19$$$.

The prime factorization is $$$4864 = 2^{8} \cdot 19$$$A.