Prime factorization of $$$4828$$$

Find the prime factorization of $$$4828$$$.

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

Determine whether $$$4828$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4828$$$ by $$${\color{green}2}$$$: $$$\frac{4828}{2} = {\color{red}2414}$$$.

Determine whether $$$2414$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2414$$$ by $$${\color{green}2}$$$: $$$\frac{2414}{2} = {\color{red}1207}$$$.

Determine whether $$$1207$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1207$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1207$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1207$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1207$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1207$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$1207$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$1207$$$ by $$${\color{green}17}$$$: $$$\frac{1207}{17} = {\color{red}71}$$$.

The prime number $$${\color{green}71}$$$ has no other factors then $$$1$$$ and $$${\color{green}71}$$$: $$$\frac{71}{71} = {\color{red}1}$$$.

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: $$$4828 = 2^{2} \cdot 17 \cdot 71$$$.

The prime factorization is $$$4828 = 2^{2} \cdot 17 \cdot 71$$$A.