Prime factorization of $$$4706$$$

Find the prime factorization of $$$4706$$$.

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

Determine whether $$$4706$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4706$$$ by $$${\color{green}2}$$$: $$$\frac{4706}{2} = {\color{red}2353}$$$.

Determine whether $$$2353$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2353$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2353$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2353$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2353$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$2353$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$2353$$$ by $$${\color{green}13}$$$: $$$\frac{2353}{13} = {\color{red}181}$$$.

The prime number $$${\color{green}181}$$$ has no other factors then $$$1$$$ and $$${\color{green}181}$$$: $$$\frac{181}{181} = {\color{red}1}$$$.

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: $$$4706 = 2 \cdot 13 \cdot 181$$$.

The prime factorization is $$$4706 = 2 \cdot 13 \cdot 181$$$A.