Prime factorization of $$$2709$$$

Find the prime factorization of $$$2709$$$.

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

Determine whether $$$2709$$$ is divisible by $$$2$$$.

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

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

Determine whether $$$2709$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$2709$$$ by $$${\color{green}3}$$$: $$$\frac{2709}{3} = {\color{red}903}$$$.

Determine whether $$$903$$$ is divisible by $$$3$$$.

It is divisible, thus, divide $$$903$$$ by $$${\color{green}3}$$$: $$$\frac{903}{3} = {\color{red}301}$$$.

Determine whether $$$301$$$ is divisible by $$$3$$$.

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

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

Determine whether $$$301$$$ is divisible by $$$5$$$.

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

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

Determine whether $$$301$$$ is divisible by $$$7$$$.

It is divisible, thus, divide $$$301$$$ by $$${\color{green}7}$$$: $$$\frac{301}{7} = {\color{red}43}$$$.

The prime number $$${\color{green}43}$$$ has no other factors then $$$1$$$ and $$${\color{green}43}$$$: $$$\frac{43}{43} = {\color{red}1}$$$.

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: $$$2709 = 3^{2} \cdot 7 \cdot 43$$$.

The prime factorization is $$$2709 = 3^{2} \cdot 7 \cdot 43$$$A.