Prime factorization of $$$3675$$$

Find the prime factorization of $$$3675$$$.

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

Determine whether $$$3675$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$3675$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$3675$$$ by $$${\color{green}3}$$$: $$$\frac{3675}{3} = {\color{red}1225}$$$.

Determine whether $$$1225$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$1225$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$1225$$$ by $$${\color{green}5}$$$: $$$\frac{1225}{5} = {\color{red}245}$$$.

Determine whether $$$245$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$245$$$ by $$${\color{green}5}$$$: $$$\frac{245}{5} = {\color{red}49}$$$.

Determine whether $$$49$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$49$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$49$$$ by $$${\color{green}7}$$$: $$$\frac{49}{7} = {\color{red}7}$$$.

The prime number $$${\color{green}7}$$$ has no other factors then $$$1$$$ and $$${\color{green}7}$$$: $$$\frac{7}{7} = {\color{red}1}$$$.

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: $$$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$$.

The prime factorization is $$$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$$A.