Prime factorization of $$$824$$$

Find the prime factorization of $$$824$$$.

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

Determine whether $$$824$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$824$$$ by $$${\color{green}2}$$$: $$$\frac{824}{2} = {\color{red}412}$$$.

Determine whether $$$412$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$412$$$ by $$${\color{green}2}$$$: $$$\frac{412}{2} = {\color{red}206}$$$.

Determine whether $$$206$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$206$$$ by $$${\color{green}2}$$$: $$$\frac{206}{2} = {\color{red}103}$$$.

The prime number $$${\color{green}103}$$$ has no other factors then $$$1$$$ and $$${\color{green}103}$$$: $$$\frac{103}{103} = {\color{red}1}$$$.

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: $$$824 = 2^{3} \cdot 103$$$.

The prime factorization is $$$824 = 2^{3} \cdot 103$$$A.