Prime factorization of $$$4235$$$

Find the prime factorization of $$$4235$$$.

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

Determine whether $$$4235$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$4235$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$4235$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$4235$$$ by $$${\color{green}5}$$$: $$$\frac{4235}{5} = {\color{red}847}$$$.

Determine whether $$$847$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$847$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$847$$$ by $$${\color{green}7}$$$: $$$\frac{847}{7} = {\color{red}121}$$$.

Determine whether $$$121$$$ is divisible by $$$7$$$.

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

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

Determine whether $$$121$$$ is divisible by $$$11$$$.

It is divisible, thus, divide $$$121$$$ by $$${\color{green}11}$$$: $$$\frac{121}{11} = {\color{red}11}$$$.

The prime number $$${\color{green}11}$$$ has no other factors then $$$1$$$ and $$${\color{green}11}$$$: $$$\frac{11}{11} = {\color{red}1}$$$.

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: $$$4235 = 5 \cdot 7 \cdot 11^{2}$$$.

The prime factorization is $$$4235 = 5 \cdot 7 \cdot 11^{2}$$$A.