Prime factorization of $$$4776$$$

Find the prime factorization of $$$4776$$$.

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

Determine whether $$$4776$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4776$$$ by $$${\color{green}2}$$$: $$$\frac{4776}{2} = {\color{red}2388}$$$.

Determine whether $$$2388$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2388$$$ by $$${\color{green}2}$$$: $$$\frac{2388}{2} = {\color{red}1194}$$$.

Determine whether $$$1194$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1194$$$ by $$${\color{green}2}$$$: $$$\frac{1194}{2} = {\color{red}597}$$$.

Determine whether $$$597$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$597$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$597$$$ by $$${\color{green}3}$$$: $$$\frac{597}{3} = {\color{red}199}$$$.

The prime number $$${\color{green}199}$$$ has no other factors then $$$1$$$ and $$${\color{green}199}$$$: $$$\frac{199}{199} = {\color{red}1}$$$.

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: $$$4776 = 2^{3} \cdot 3 \cdot 199$$$.

The prime factorization is $$$4776 = 2^{3} \cdot 3 \cdot 199$$$A.