Prime factorization of $$$1776$$$

Find the prime factorization of $$$1776$$$.

Start with the number $$$2$$$.

Determine whether $$$1776$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1776$$$ by $$${\color{green}2}$$$: $$$\frac{1776}{2} = {\color{red}888}$$$.

Determine whether $$$888$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$888$$$ by $$${\color{green}2}$$$: $$$\frac{888}{2} = {\color{red}444}$$$.

Determine whether $$$444$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$444$$$ by $$${\color{green}2}$$$: $$$\frac{444}{2} = {\color{red}222}$$$.

Determine whether $$$222$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$222$$$ by $$${\color{green}2}$$$: $$$\frac{222}{2} = {\color{red}111}$$$.

Determine whether $$$111$$$ is divisible by $$$2$$$.

Since it is not divisible, move to the next prime number.

The next prime number is $$$3$$$.

Determine whether $$$111$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$111$$$ by $$${\color{green}3}$$$: $$$\frac{111}{3} = {\color{red}37}$$$.

The prime number $$${\color{green}37}$$$ has no other factors then $$$1$$$ and $$${\color{green}37}$$$: $$$\frac{37}{37} = {\color{red}1}$$$.

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: $$$1776 = 2^{4} \cdot 3 \cdot 37$$$.

The prime factorization is $$$1776 = 2^{4} \cdot 3 \cdot 37$$$A.