Prime factorization of $$$1635$$$

Find the prime factorization of $$$1635$$$.

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

Determine whether $$$1635$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1635$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1635$$$ by $$${\color{green}3}$$$: $$$\frac{1635}{3} = {\color{red}545}$$$.

Determine whether $$$545$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$545$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$545$$$ by $$${\color{green}5}$$$: $$$\frac{545}{5} = {\color{red}109}$$$.

The prime number $$${\color{green}109}$$$ has no other factors then $$$1$$$ and $$${\color{green}109}$$$: $$$\frac{109}{109} = {\color{red}1}$$$.

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: $$$1635 = 3 \cdot 5 \cdot 109$$$.

The prime factorization is $$$1635 = 3 \cdot 5 \cdot 109$$$A.