Prime factorization of $$$4772$$$

Find the prime factorization of $$$4772$$$.

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

Determine whether $$$4772$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4772$$$ by $$${\color{green}2}$$$: $$$\frac{4772}{2} = {\color{red}2386}$$$.

Determine whether $$$2386$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2386$$$ by $$${\color{green}2}$$$: $$$\frac{2386}{2} = {\color{red}1193}$$$.

The prime number $$${\color{green}1193}$$$ has no other factors then $$$1$$$ and $$${\color{green}1193}$$$: $$$\frac{1193}{1193} = {\color{red}1}$$$.

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: $$$4772 = 2^{2} \cdot 1193$$$.

The prime factorization is $$$4772 = 2^{2} \cdot 1193$$$A.