Prime factorization of $$$1272$$$
Your Input
Find the prime factorization of $$$1272$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1272$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1272$$$ by $$${\color{green}2}$$$: $$$\frac{1272}{2} = {\color{red}636}$$$.
Determine whether $$$636$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$636$$$ by $$${\color{green}2}$$$: $$$\frac{636}{2} = {\color{red}318}$$$.
Determine whether $$$318$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$318$$$ by $$${\color{green}2}$$$: $$$\frac{318}{2} = {\color{red}159}$$$.
Determine whether $$$159$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$159$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$159$$$ by $$${\color{green}3}$$$: $$$\frac{159}{3} = {\color{red}53}$$$.
The prime number $$${\color{green}53}$$$ has no other factors then $$$1$$$ and $$${\color{green}53}$$$: $$$\frac{53}{53} = {\color{red}1}$$$.
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: $$$1272 = 2^{3} \cdot 3 \cdot 53$$$.
Answer
The prime factorization is $$$1272 = 2^{3} \cdot 3 \cdot 53$$$A.