Prime factorization of $$$4844$$$

Find the prime factorization of $$$4844$$$.

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

Determine whether $$$4844$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4844$$$ by $$${\color{green}2}$$$: $$$\frac{4844}{2} = {\color{red}2422}$$$.

Determine whether $$$2422$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2422$$$ by $$${\color{green}2}$$$: $$$\frac{2422}{2} = {\color{red}1211}$$$.

Determine whether $$$1211$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1211$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1211$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1211$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$1211$$$ by $$${\color{green}7}$$$: $$$\frac{1211}{7} = {\color{red}173}$$$.

The prime number $$${\color{green}173}$$$ has no other factors then $$$1$$$ and $$${\color{green}173}$$$: $$$\frac{173}{173} = {\color{red}1}$$$.

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: $$$4844 = 2^{2} \cdot 7 \cdot 173$$$.

The prime factorization is $$$4844 = 2^{2} \cdot 7 \cdot 173$$$A.