# Prime factorization of $2709$

The calculator will find the prime factorization of $2709$, with steps shown.

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Find the prime factorization of $2709$.

### Solution

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.