Prime factorization of $$$1862$$$
Your Input
Find the prime factorization of $$$1862$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1862$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1862$$$ by $$${\color{green}2}$$$: $$$\frac{1862}{2} = {\color{red}931}$$$.
Determine whether $$$931$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$931$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$931$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$931$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$931$$$ by $$${\color{green}7}$$$: $$$\frac{931}{7} = {\color{red}133}$$$.
Determine whether $$$133$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$133$$$ by $$${\color{green}7}$$$: $$$\frac{133}{7} = {\color{red}19}$$$.
The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.
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: $$$1862 = 2 \cdot 7^{2} \cdot 19$$$.
Answer
The prime factorization is $$$1862 = 2 \cdot 7^{2} \cdot 19$$$A.