Prime factorization of $$$2824$$$

Find the prime factorization of $$$2824$$$.

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

Determine whether $$$2824$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2824$$$ by $$${\color{green}2}$$$: $$$\frac{2824}{2} = {\color{red}1412}$$$.

Determine whether $$$1412$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1412$$$ by $$${\color{green}2}$$$: $$$\frac{1412}{2} = {\color{red}706}$$$.

Determine whether $$$706$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$706$$$ by $$${\color{green}2}$$$: $$$\frac{706}{2} = {\color{red}353}$$$.

The prime number $$${\color{green}353}$$$ has no other factors then $$$1$$$ and $$${\color{green}353}$$$: $$$\frac{353}{353} = {\color{red}1}$$$.

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: $$$2824 = 2^{3} \cdot 353$$$.

The prime factorization is $$$2824 = 2^{3} \cdot 353$$$A.