Prime factorization of $$$1629$$$

Find the prime factorization of $$$1629$$$.

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

Determine whether $$$1629$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$1629$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$1629$$$ by $$${\color{green}3}$$$: $$$\frac{1629}{3} = {\color{red}543}$$$.

Determine whether $$$543$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$543$$$ by $$${\color{green}3}$$$: $$$\frac{543}{3} = {\color{red}181}$$$.

The prime number $$${\color{green}181}$$$ has no other factors then $$$1$$$ and $$${\color{green}181}$$$: $$$\frac{181}{181} = {\color{red}1}$$$.

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: $$$1629 = 3^{2} \cdot 181$$$.

The prime factorization is $$$1629 = 3^{2} \cdot 181$$$A.