Prime factorization of $$$1578$$$
Your Input
Find the prime factorization of $$$1578$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1578$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1578$$$ by $$${\color{green}2}$$$: $$$\frac{1578}{2} = {\color{red}789}$$$.
Determine whether $$$789$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$789$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$789$$$ by $$${\color{green}3}$$$: $$$\frac{789}{3} = {\color{red}263}$$$.
The prime number $$${\color{green}263}$$$ has no other factors then $$$1$$$ and $$${\color{green}263}$$$: $$$\frac{263}{263} = {\color{red}1}$$$.
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: $$$1578 = 2 \cdot 3 \cdot 263$$$.
Answer
The prime factorization is $$$1578 = 2 \cdot 3 \cdot 263$$$A.