Prime factorization of $$$4845$$$

Find the prime factorization of $$$4845$$$.

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

Determine whether $$$4845$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4845$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4845$$$ by $$${\color{green}3}$$$: $$$\frac{4845}{3} = {\color{red}1615}$$$.

Determine whether $$$1615$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1615$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1615$$$ by $$${\color{green}5}$$$: $$$\frac{1615}{5} = {\color{red}323}$$$.

Determine whether $$$323$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$323$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$323$$$ is divisible by $$$11$$$.

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

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

Determine whether $$$323$$$ is divisible by $$$13$$$.

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

The next prime number is $$$17$$$.

Determine whether $$$323$$$ is divisible by $$$17$$$.

It is divisible, thus, divide $$$323$$$ by $$${\color{green}17}$$$: $$$\frac{323}{17} = {\color{red}19}$$$.

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: $$$4845 = 3 \cdot 5 \cdot 17 \cdot 19$$$.

The prime factorization is $$$4845 = 3 \cdot 5 \cdot 17 \cdot 19$$$A.