Prime factorization of $$$4888$$$

Find the prime factorization of $$$4888$$$.

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

Determine whether $$$4888$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4888$$$ by $$${\color{green}2}$$$: $$$\frac{4888}{2} = {\color{red}2444}$$$.

Determine whether $$$2444$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2444$$$ by $$${\color{green}2}$$$: $$$\frac{2444}{2} = {\color{red}1222}$$$.

Determine whether $$$1222$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1222$$$ by $$${\color{green}2}$$$: $$$\frac{1222}{2} = {\color{red}611}$$$.

Determine whether $$$611$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$611$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$611$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$611$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$611$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$611$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$611$$$ by $$${\color{green}13}$$$: $$$\frac{611}{13} = {\color{red}47}$$$.

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: $$$4888 = 2^{3} \cdot 13 \cdot 47$$$.

The prime factorization is $$$4888 = 2^{3} \cdot 13 \cdot 47$$$A.