Prime factorization of $$$3780$$$
Your Input
Find the prime factorization of $$$3780$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3780$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3780$$$ by $$${\color{green}2}$$$: $$$\frac{3780}{2} = {\color{red}1890}$$$.
Determine whether $$$1890$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1890$$$ by $$${\color{green}2}$$$: $$$\frac{1890}{2} = {\color{red}945}$$$.
Determine whether $$$945$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$945$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$945$$$ by $$${\color{green}3}$$$: $$$\frac{945}{3} = {\color{red}315}$$$.
Determine whether $$$315$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$315$$$ by $$${\color{green}3}$$$: $$$\frac{315}{3} = {\color{red}105}$$$.
Determine whether $$$105$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$105$$$ by $$${\color{green}3}$$$: $$$\frac{105}{3} = {\color{red}35}$$$.
Determine whether $$$35$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$35$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$35$$$ by $$${\color{green}5}$$$: $$$\frac{35}{5} = {\color{red}7}$$$.
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: $$$3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7$$$.
Answer
The prime factorization is $$$3780 = 2^{2} \cdot 3^{3} \cdot 5 \cdot 7$$$A.