Prime factorization of $$$2632$$$
Your Input
Find the prime factorization of $$$2632$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2632$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2632$$$ by $$${\color{green}2}$$$: $$$\frac{2632}{2} = {\color{red}1316}$$$.
Determine whether $$$1316$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1316$$$ by $$${\color{green}2}$$$: $$$\frac{1316}{2} = {\color{red}658}$$$.
Determine whether $$$658$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$658$$$ by $$${\color{green}2}$$$: $$$\frac{658}{2} = {\color{red}329}$$$.
Determine whether $$$329$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$329$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$329$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$329$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$329$$$ by $$${\color{green}7}$$$: $$$\frac{329}{7} = {\color{red}47}$$$.
The prime number $$${\color{green}47}$$$ has no other factors then $$$1$$$ and $$${\color{green}47}$$$: $$$\frac{47}{47} = {\color{red}1}$$$.
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: $$$2632 = 2^{3} \cdot 7 \cdot 47$$$.
Answer
The prime factorization is $$$2632 = 2^{3} \cdot 7 \cdot 47$$$A.