Prime factorization of $$$3470$$$
Your Input
Find the prime factorization of $$$3470$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$3470$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$3470$$$ by $$${\color{green}2}$$$: $$$\frac{3470}{2} = {\color{red}1735}$$$.
Determine whether $$$1735$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$1735$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$1735$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$1735$$$ by $$${\color{green}5}$$$: $$$\frac{1735}{5} = {\color{red}347}$$$.
The prime number $$${\color{green}347}$$$ has no other factors then $$$1$$$ and $$${\color{green}347}$$$: $$$\frac{347}{347} = {\color{red}1}$$$.
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: $$$3470 = 2 \cdot 5 \cdot 347$$$.
Answer
The prime factorization is $$$3470 = 2 \cdot 5 \cdot 347$$$A.