Prime factorization of $$$1176$$$

Find the prime factorization of $$$1176$$$.

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

Determine whether $$$1176$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1176$$$ by $$${\color{green}2}$$$: $$$\frac{1176}{2} = {\color{red}588}$$$.

Determine whether $$$588$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$588$$$ by $$${\color{green}2}$$$: $$$\frac{588}{2} = {\color{red}294}$$$.

Determine whether $$$294$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$294$$$ by $$${\color{green}2}$$$: $$$\frac{294}{2} = {\color{red}147}$$$.

Determine whether $$$147$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$147$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$147$$$ by $$${\color{green}3}$$$: $$$\frac{147}{3} = {\color{red}49}$$$.

Determine whether $$$49$$$ is divisible by $$$3$$$.

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

The next prime number is $$$5$$$.

Determine whether $$$49$$$ is divisible by $$$5$$$.

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

The next prime number is $$$7$$$.

Determine whether $$$49$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$1176 = 2^{3} \cdot 3 \cdot 7^{2}$$$.

The prime factorization is $$$1176 = 2^{3} \cdot 3 \cdot 7^{2}$$$A.