Prime factorization of $$$1650$$$
Your Input
Find the prime factorization of $$$1650$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$1650$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1650$$$ by $$${\color{green}2}$$$: $$$\frac{1650}{2} = {\color{red}825}$$$.
Determine whether $$$825$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$825$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$825$$$ by $$${\color{green}3}$$$: $$$\frac{825}{3} = {\color{red}275}$$$.
Determine whether $$$275$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$275$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$275$$$ by $$${\color{green}5}$$$: $$$\frac{275}{5} = {\color{red}55}$$$.
Determine whether $$$55$$$ is divisible by $$$5$$$.
It is divisible, thus, divide $$$55$$$ by $$${\color{green}5}$$$: $$$\frac{55}{5} = {\color{red}11}$$$.
The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.
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: $$$1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11$$$.
Answer
The prime factorization is $$$1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11$$$A.