Prime factorization of $$$1870$$$
Your Input
Find the prime factorization of $$$1870$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1870$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1870$$$ by $$${\color{green}2}$$$: $$$\frac{1870}{2} = {\color{red}935}$$$.
Determine whether $$$935$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$935$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$935$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$935$$$ by $$${\color{green}5}$$$: $$$\frac{935}{5} = {\color{red}187}$$$.
Determine whether $$$187$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$187$$$ is divisible by $$$7$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$11$$$.
Determine whether $$$187$$$ is divisible by $$$11$$$.
It is divisible, thus, divide $$$187$$$ by $$${\color{green}11}$$$: $$$\frac{187}{11} = {\color{red}17}$$$.
The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.
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: $$$1870 = 2 \cdot 5 \cdot 11 \cdot 17$$$.
Answer
The prime factorization is $$$1870 = 2 \cdot 5 \cdot 11 \cdot 17$$$A.