Prime factorization of $$$1235$$$

Find the prime factorization of $$$1235$$$.

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

Determine whether $$$1235$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1235$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1235$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1235$$$ by $$${\color{green}5}$$$: $$$\frac{1235}{5} = {\color{red}247}$$$.

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: $$$1235 = 5 \cdot 13 \cdot 19$$$.

The prime factorization is $$$1235 = 5 \cdot 13 \cdot 19$$$A.