Prime factorization of $$$4484$$$

Find the prime factorization of $$$4484$$$.

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

Determine whether $$$4484$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4484$$$ by $$${\color{green}2}$$$: $$$\frac{4484}{2} = {\color{red}2242}$$$.

Determine whether $$$2242$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2242$$$ by $$${\color{green}2}$$$: $$$\frac{2242}{2} = {\color{red}1121}$$$.

Determine whether $$$1121$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1121$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1121$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$1121$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$1121$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$1121$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$1121$$$ is divisible by $$$17$$$.

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

The next prime number is $$$19$$$.

Determine whether $$$1121$$$ is divisible by $$$19$$$.

It is divisible, thus, divide $$$1121$$$ by $$${\color{green}19}$$$: $$$\frac{1121}{19} = {\color{red}59}$$$.

The prime number $$${\color{green}59}$$$ has no other factors then $$$1$$$ and $$${\color{green}59}$$$: $$$\frac{59}{59} = {\color{red}1}$$$.

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: $$$4484 = 2^{2} \cdot 19 \cdot 59$$$.

The prime factorization is $$$4484 = 2^{2} \cdot 19 \cdot 59$$$A.