Prime factorization of $$$4454$$$

Find the prime factorization of $$$4454$$$.

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

Determine whether $$$4454$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4454$$$ by $$${\color{green}2}$$$: $$$\frac{4454}{2} = {\color{red}2227}$$$.

Determine whether $$$2227$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2227$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$2227$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$2227$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$2227$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$2227$$$ is divisible by $$$13$$$.

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

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

Determine whether $$$2227$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$2227$$$ by $$${\color{green}17}$$$: $$$\frac{2227}{17} = {\color{red}131}$$$.

The prime number $$${\color{green}131}$$$ has no other factors then $$$1$$$ and $$${\color{green}131}$$$: $$$\frac{131}{131} = {\color{red}1}$$$.

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: $$$4454 = 2 \cdot 17 \cdot 131$$$.

The prime factorization is $$$4454 = 2 \cdot 17 \cdot 131$$$A.