Prime factorization of $$$1251$$$

Find the prime factorization of $$$1251$$$.

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

Determine whether $$$1251$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1251$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1251$$$ by $$${\color{green}3}$$$: $$$\frac{1251}{3} = {\color{red}417}$$$.

Determine whether $$$417$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$417$$$ by $$${\color{green}3}$$$: $$$\frac{417}{3} = {\color{red}139}$$$.

The prime number $$${\color{green}139}$$$ has no other factors then $$$1$$$ and $$${\color{green}139}$$$: $$$\frac{139}{139} = {\color{red}1}$$$.

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: $$$1251 = 3^{2} \cdot 139$$$.

The prime factorization is $$$1251 = 3^{2} \cdot 139$$$A.