Prime factorization of $$$4176$$$

Find the prime factorization of $$$4176$$$.

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

Determine whether $$$4176$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$4176$$$ by $$${\color{green}2}$$$: $$$\frac{4176}{2} = {\color{red}2088}$$$.

Determine whether $$$2088$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$2088$$$ by $$${\color{green}2}$$$: $$$\frac{2088}{2} = {\color{red}1044}$$$.

Determine whether $$$1044$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1044$$$ by $$${\color{green}2}$$$: $$$\frac{1044}{2} = {\color{red}522}$$$.

Determine whether $$$522$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$522$$$ by $$${\color{green}2}$$$: $$$\frac{522}{2} = {\color{red}261}$$$.

Determine whether $$$261$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$261$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$261$$$ by $$${\color{green}3}$$$: $$$\frac{261}{3} = {\color{red}87}$$$.

Determine whether $$$87$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$87$$$ by $$${\color{green}3}$$$: $$$\frac{87}{3} = {\color{red}29}$$$.

The prime number $$${\color{green}29}$$$ has no other factors then $$$1$$$ and $$${\color{green}29}$$$: $$$\frac{29}{29} = {\color{red}1}$$$.

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: $$$4176 = 2^{4} \cdot 3^{2} \cdot 29$$$.

The prime factorization is $$$4176 = 2^{4} \cdot 3^{2} \cdot 29$$$A.