# Prime factorization of $2727$

The calculator will find the prime factorization of $2727$, with steps shown.

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Find the prime factorization of $2727$.

### Solution

Start with the number $2$.

Determine whether $2727$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2727$ is divisible by $3$.

It is divisible, thus, divide $2727$ by ${\color{green}3}$: $\frac{2727}{3} = {\color{red}909}$.

Determine whether $909$ is divisible by $3$.

It is divisible, thus, divide $909$ by ${\color{green}3}$: $\frac{909}{3} = {\color{red}303}$.

Determine whether $303$ is divisible by $3$.

It is divisible, thus, divide $303$ by ${\color{green}3}$: $\frac{303}{3} = {\color{red}101}$.

The prime number ${\color{green}101}$ has no other factors then $1$ and ${\color{green}101}$: $\frac{101}{101} = {\color{red}1}$.

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: $2727 = 3^{3} \cdot 101$.

The prime factorization is $2727 = 3^{3} \cdot 101$A.