Prime factorization of $$$2772$$$
Your Input
Find the prime factorization of $$$2772$$$.
Solution
Start with the number $$$2$$$.
Determine whether $$$2772$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$2772$$$ by $$${\color{green}2}$$$: $$$\frac{2772}{2} = {\color{red}1386}$$$.
Determine whether $$$1386$$$ is divisible by $$$2$$$.
It is divisible, thus, divide $$$1386$$$ by $$${\color{green}2}$$$: $$$\frac{1386}{2} = {\color{red}693}$$$.
Determine whether $$$693$$$ is divisible by $$$2$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$3$$$.
Determine whether $$$693$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$693$$$ by $$${\color{green}3}$$$: $$$\frac{693}{3} = {\color{red}231}$$$.
Determine whether $$$231$$$ is divisible by $$$3$$$.
It is divisible, thus, divide $$$231$$$ by $$${\color{green}3}$$$: $$$\frac{231}{3} = {\color{red}77}$$$.
Determine whether $$$77$$$ is divisible by $$$3$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$5$$$.
Determine whether $$$77$$$ is divisible by $$$5$$$.
Since it is not divisible, move to the next prime number.
The next prime number is $$$7$$$.
Determine whether $$$77$$$ is divisible by $$$7$$$.
It is divisible, thus, divide $$$77$$$ by $$${\color{green}7}$$$: $$$\frac{77}{7} = {\color{red}11}$$$.
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: $$$2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11$$$.
Answer
The prime factorization is $$$2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11$$$A.