Prime factorization of $$$2772$$$

Find the prime factorization of $$$2772$$$.

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: $$$2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11$$$.

The prime factorization is $$$2772 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 11$$$A.