Prime factorization of $$$4695$$$

Find the prime factorization of $$$4695$$$.

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

Determine whether $$$4695$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4695$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$4695$$$ by $$${\color{green}3}$$$: $$$\frac{4695}{3} = {\color{red}1565}$$$.

Determine whether $$$1565$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1565$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1565$$$ by $$${\color{green}5}$$$: $$$\frac{1565}{5} = {\color{red}313}$$$.

The prime number $$${\color{green}313}$$$ has no other factors then $$$1$$$ and $$${\color{green}313}$$$: $$$\frac{313}{313} = {\color{red}1}$$$.

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: $$$4695 = 3 \cdot 5 \cdot 313$$$.

The prime factorization is $$$4695 = 3 \cdot 5 \cdot 313$$$A.