Prime factorization of $$$4906$$$

Find the prime factorization of $$$4906$$$.

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

Determine whether $$$4906$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4906$$$ by $$${\color{green}2}$$$: $$$\frac{4906}{2} = {\color{red}2453}$$$.

Determine whether $$$2453$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2453$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2453$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2453$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2453$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$2453$$$ by $$${\color{green}11}$$$: $$$\frac{2453}{11} = {\color{red}223}$$$.

The prime number $$${\color{green}223}$$$ has no other factors then $$$1$$$ and $$${\color{green}223}$$$: $$$\frac{223}{223} = {\color{red}1}$$$.

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: $$$4906 = 2 \cdot 11 \cdot 223$$$.

The prime factorization is $$$4906 = 2 \cdot 11 \cdot 223$$$A.