Prime factorization of $$$3952$$$

Find the prime factorization of $$$3952$$$.

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

Determine whether $$$3952$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$3952$$$ by $$${\color{green}2}$$$: $$$\frac{3952}{2} = {\color{red}1976}$$$.

Determine whether $$$1976$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$1976$$$ by $$${\color{green}2}$$$: $$$\frac{1976}{2} = {\color{red}988}$$$.

Determine whether $$$988$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$988$$$ by $$${\color{green}2}$$$: $$$\frac{988}{2} = {\color{red}494}$$$.

Determine whether $$$494$$$ is divisible by $$$2$$$.

It is divisible, thus, divide $$$494$$$ by $$${\color{green}2}$$$: $$$\frac{494}{2} = {\color{red}247}$$$.

Determine whether $$$247$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$247$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$247$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$247$$$ is divisible by $$$7$$$.

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

The next prime number is $$$11$$$.

Determine whether $$$247$$$ is divisible by $$$11$$$.

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

The next prime number is $$$13$$$.

Determine whether $$$247$$$ is divisible by $$$13$$$.

It is divisible, thus, divide $$$247$$$ by $$${\color{green}13}$$$: $$$\frac{247}{13} = {\color{red}19}$$$.

The prime number $$${\color{green}19}$$$ has no other factors then $$$1$$$ and $$${\color{green}19}$$$: $$$\frac{19}{19} = {\color{red}1}$$$.

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: $$$3952 = 2^{4} \cdot 13 \cdot 19$$$.

The prime factorization is $$$3952 = 2^{4} \cdot 13 \cdot 19$$$A.