Prime factorization of $$$4653$$$

Find the prime factorization of $$$4653$$$.

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

Determine whether $$$4653$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4653$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4653$$$ by $$${\color{green}3}$$$: $$$\frac{4653}{3} = {\color{red}1551}$$$.

Determine whether $$$1551$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1551$$$ by $$${\color{green}3}$$$: $$$\frac{1551}{3} = {\color{red}517}$$$.

Determine whether $$$517$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$517$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$517$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$517$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$517$$$ by $$${\color{green}11}$$$: $$$\frac{517}{11} = {\color{red}47}$$$.

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: $$$4653 = 3^{2} \cdot 11 \cdot 47$$$.

The prime factorization is $$$4653 = 3^{2} \cdot 11 \cdot 47$$$A.