Prime factorization of $$$1392$$$

Find the prime factorization of $$$1392$$$.

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

Determine whether $$$1392$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1392$$$ by $$${\color{green}2}$$$: $$$\frac{1392}{2} = {\color{red}696}$$$.

Determine whether $$$696$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$696$$$ by $$${\color{green}2}$$$: $$$\frac{696}{2} = {\color{red}348}$$$.

Determine whether $$$348$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$348$$$ by $$${\color{green}2}$$$: $$$\frac{348}{2} = {\color{red}174}$$$.

Determine whether $$$174$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$174$$$ by $$${\color{green}2}$$$: $$$\frac{174}{2} = {\color{red}87}$$$.

Determine whether $$$87$$$ is divisible by $$$2$$$.

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

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

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: $$$1392 = 2^{4} \cdot 3 \cdot 29$$$.

The prime factorization is $$$1392 = 2^{4} \cdot 3 \cdot 29$$$A.