Prime factorization of $$$744$$$
Your Input
Find the prime factorization of $$$744$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$744$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$744$$$ by $$${\color{green}2}$$$: $$$\frac{744}{2} = {\color{red}372}$$$.
Determine whether $$$372$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$372$$$ by $$${\color{green}2}$$$: $$$\frac{372}{2} = {\color{red}186}$$$.
Determine whether $$$186$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$186$$$ by $$${\color{green}2}$$$: $$$\frac{186}{2} = {\color{red}93}$$$.
Determine whether $$$93$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$93$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$93$$$ by $$${\color{green}3}$$$: $$$\frac{93}{3} = {\color{red}31}$$$.
The prime number $$${\color{green}31}$$$ has no other factors then $$$1$$$ and $$${\color{green}31}$$$: $$$\frac{31}{31} = {\color{red}1}$$$.
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: $$$744 = 2^{3} \cdot 3 \cdot 31$$$.
Answer
The prime factorization is $$$744 = 2^{3} \cdot 3 \cdot 31$$$A.