Prime factorization of $$$4770$$$

Find the prime factorization of $$$4770$$$.

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

Determine whether $$$4770$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4770$$$ by $$${\color{green}2}$$$: $$$\frac{4770}{2} = {\color{red}2385}$$$.

Determine whether $$$2385$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2385$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2385$$$ by $$${\color{green}3}$$$: $$$\frac{2385}{3} = {\color{red}795}$$$.

Determine whether $$$795$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$795$$$ by $$${\color{green}3}$$$: $$$\frac{795}{3} = {\color{red}265}$$$.

Determine whether $$$265$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$265$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$265$$$ by $$${\color{green}5}$$$: $$$\frac{265}{5} = {\color{red}53}$$$.

The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.

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: $$$4770 = 2 \cdot 3^{2} \cdot 5 \cdot 53$$$.

The prime factorization is $$$4770 = 2 \cdot 3^{2} \cdot 5 \cdot 53$$$A.