Prime factorization of $$$444$$$
Your Input
Find the prime factorization of $$$444$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$444$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$444$$$ by $$${\color{green}2}$$$: $$$\frac{444}{2} = {\color{red}222}$$$.
Determine whether $$$222$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$222$$$ by $$${\color{green}2}$$$: $$$\frac{222}{2} = {\color{red}111}$$$.
Determine whether $$$111$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$111$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$111$$$ by $$${\color{green}3}$$$: $$$\frac{111}{3} = {\color{red}37}$$$.
The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.
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: $$$444 = 2^{2} \cdot 3 \cdot 37$$$.
Answer
The prime factorization is $$$444 = 2^{2} \cdot 3 \cdot 37$$$A.