# Prime factorization of $3270$

The calculator will find the prime factorization of $3270$, with steps shown.

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Find the prime factorization of $3270$.

### Solution

Start with the number $2$.

Determine whether $3270$ is divisible by $2$.

It is divisible, thus, divide $3270$ by ${\color{green}2}$: $\frac{3270}{2} = {\color{red}1635}$.

Determine whether $1635$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1635$ is divisible by $3$.

It is divisible, thus, divide $1635$ by ${\color{green}3}$: $\frac{1635}{3} = {\color{red}545}$.

Determine whether $545$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $545$ is divisible by $5$.

It is divisible, thus, divide $545$ by ${\color{green}5}$: $\frac{545}{5} = {\color{red}109}$.

The prime number ${\color{green}109}$ has no other factors then $1$ and ${\color{green}109}$: $\frac{109}{109} = {\color{red}1}$.

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: $3270 = 2 \cdot 3 \cdot 5 \cdot 109$.

The prime factorization is $3270 = 2 \cdot 3 \cdot 5 \cdot 109$A.