Prime factorization of $$$4494$$$

Find the prime factorization of $$$4494$$$.

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

Determine whether $$$4494$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4494$$$ by $$${\color{green}2}$$$: $$$\frac{4494}{2} = {\color{red}2247}$$$.

Determine whether $$$2247$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2247$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2247$$$ by $$${\color{green}3}$$$: $$$\frac{2247}{3} = {\color{red}749}$$$.

Determine whether $$$749$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$749$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$749$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$749$$$ by $$${\color{green}7}$$$: $$$\frac{749}{7} = {\color{red}107}$$$.

The prime number $$${\color{green}107}$$$ has no other factors then $$$1$$$ and $$${\color{green}107}$$$: $$$\frac{107}{107} = {\color{red}1}$$$.

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: $$$4494 = 2 \cdot 3 \cdot 7 \cdot 107$$$.

The prime factorization is $$$4494 = 2 \cdot 3 \cdot 7 \cdot 107$$$A.