Prime factorization of $$$126$$$

Find the prime factorization of $$$126$$$.

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: $$$126 = 2 \cdot 3^{2} \cdot 7$$$.

The prime factorization is $$$126 = 2 \cdot 3^{2} \cdot 7$$$A.