Prime factorization of $$$3568$$$

Find the prime factorization of $$$3568$$$.

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

Determine whether $$$3568$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3568$$$ by $$${\color{green}2}$$$: $$$\frac{3568}{2} = {\color{red}1784}$$$.

Determine whether $$$1784$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1784$$$ by $$${\color{green}2}$$$: $$$\frac{1784}{2} = {\color{red}892}$$$.

Determine whether $$$892$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$892$$$ by $$${\color{green}2}$$$: $$$\frac{892}{2} = {\color{red}446}$$$.

Determine whether $$$446$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$446$$$ by $$${\color{green}2}$$$: $$$\frac{446}{2} = {\color{red}223}$$$.

The prime number $$${\color{green}223}$$$ has no other factors then $$$1$$$ and $$${\color{green}223}$$$: $$$\frac{223}{223} = {\color{red}1}$$$.

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: $$$3568 = 2^{4} \cdot 223$$$.

The prime factorization is $$$3568 = 2^{4} \cdot 223$$$A.