Prime factorization of $$$3878$$$
Your Input
Find the prime factorization of $$$3878$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3878$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3878$$$ by $$${\color{green}2}$$$: $$$\frac{3878}{2} = {\color{red}1939}$$$.
Determine whether $$$1939$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1939$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1939$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$1939$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$1939$$$ by $$${\color{green}7}$$$: $$$\frac{1939}{7} = {\color{red}277}$$$.
The prime number $$${\color{green}277}$$$ has no other factors then $$$1$$$ and $$${\color{green}277}$$$: $$$\frac{277}{277} = {\color{red}1}$$$.
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: $$$3878 = 2 \cdot 7 \cdot 277$$$.
Answer
The prime factorization is $$$3878 = 2 \cdot 7 \cdot 277$$$A.