Prime factorization of $$$4688$$$

Find the prime factorization of $$$4688$$$.

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

Determine whether $$$4688$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4688$$$ by $$${\color{green}2}$$$: $$$\frac{4688}{2} = {\color{red}2344}$$$.

Determine whether $$$2344$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2344$$$ by $$${\color{green}2}$$$: $$$\frac{2344}{2} = {\color{red}1172}$$$.

Determine whether $$$1172$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1172$$$ by $$${\color{green}2}$$$: $$$\frac{1172}{2} = {\color{red}586}$$$.

Determine whether $$$586$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$586$$$ by $$${\color{green}2}$$$: $$$\frac{586}{2} = {\color{red}293}$$$.

The prime number $$${\color{green}293}$$$ has no other factors then $$$1$$$ and $$${\color{green}293}$$$: $$$\frac{293}{293} = {\color{red}1}$$$.

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: $$$4688 = 2^{4} \cdot 293$$$.

The prime factorization is $$$4688 = 2^{4} \cdot 293$$$A.