Prime factorization of $$$126$$$
Your Input
Find the prime factorization of $$$126$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$126$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$126$$$ by $$${\color{green}2}$$$: $$$\frac{126}{2} = {\color{red}63}$$$.
Determine whether $$$63$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$63$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$63$$$ by $$${\color{green}3}$$$: $$$\frac{63}{3} = {\color{red}21}$$$.
Determine whether $$$21$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$21$$$ by $$${\color{green}3}$$$: $$$\frac{21}{3} = {\color{red}7}$$$.
The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.
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: $$$126 = 2 \cdot 3^{2} \cdot 7$$$.
Answer
The prime factorization is $$$126 = 2 \cdot 3^{2} \cdot 7$$$A.