Prime factorization of $$$4494$$$
Your Input
Find the prime factorization of $$$4494$$$.
Solution
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: $$$4494 = 2 \cdot 3 \cdot 7 \cdot 107$$$.
Answer
The prime factorization is $$$4494 = 2 \cdot 3 \cdot 7 \cdot 107$$$A.