Prime factorization of $$$1275$$$

Find the prime factorization of $$$1275$$$.

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

Determine whether $$$1275$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1275$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1275$$$ by $$${\color{green}3}$$$: $$$\frac{1275}{3} = {\color{red}425}$$$.

Determine whether $$$425$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$425$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$425$$$ by $$${\color{green}5}$$$: $$$\frac{425}{5} = {\color{red}85}$$$.

Determine whether $$$85$$$ is divisible by $$$5$$$.

It is divisible, thus, divide $$$85$$$ by $$${\color{green}5}$$$: $$$\frac{85}{5} = {\color{red}17}$$$.

The prime number $$${\color{green}17}$$$ has no other factors then $$$1$$$ and $$${\color{green}17}$$$: $$$\frac{17}{17} = {\color{red}1}$$$.

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: $$$1275 = 3 \cdot 5^{2} \cdot 17$$$.

The prime factorization is $$$1275 = 3 \cdot 5^{2} \cdot 17$$$A.