Prime factorization of $$$4628$$$

Find the prime factorization of $$$4628$$$.

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

Determine whether $$$4628$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4628$$$ by $$${\color{green}2}$$$: $$$\frac{4628}{2} = {\color{red}2314}$$$.

Determine whether $$$2314$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2314$$$ by $$${\color{green}2}$$$: $$$\frac{2314}{2} = {\color{red}1157}$$$.

Determine whether $$$1157$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1157$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1157$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1157$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1157$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1157$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$1157$$$ by $$${\color{green}13}$$$: $$$\frac{1157}{13} = {\color{red}89}$$$.

The prime number $$${\color{green}89}$$$ has no other factors then $$$1$$$ and $$${\color{green}89}$$$: $$$\frac{89}{89} = {\color{red}1}$$$.

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: $$$4628 = 2^{2} \cdot 13 \cdot 89$$$.

The prime factorization is $$$4628 = 2^{2} \cdot 13 \cdot 89$$$A.