Prime factorization of $$$3008$$$

Find the prime factorization of $$$3008$$$.

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

Determine whether $$$3008$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3008$$$ by $$${\color{green}2}$$$: $$$\frac{3008}{2} = {\color{red}1504}$$$.

Determine whether $$$1504$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1504$$$ by $$${\color{green}2}$$$: $$$\frac{1504}{2} = {\color{red}752}$$$.

Determine whether $$$752$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$752$$$ by $$${\color{green}2}$$$: $$$\frac{752}{2} = {\color{red}376}$$$.

Determine whether $$$376$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$376$$$ by $$${\color{green}2}$$$: $$$\frac{376}{2} = {\color{red}188}$$$.

Determine whether $$$188$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$188$$$ by $$${\color{green}2}$$$: $$$\frac{188}{2} = {\color{red}94}$$$.

Determine whether $$$94$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$94$$$ by $$${\color{green}2}$$$: $$$\frac{94}{2} = {\color{red}47}$$$.

The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.

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: $$$3008 = 2^{6} \cdot 47$$$.

The prime factorization is $$$3008 = 2^{6} \cdot 47$$$A.