# Prime factorization of $2745$

The calculator will find the prime factorization of $2745$, with steps shown.

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Find the prime factorization of $2745$.

### Solution

Start with the number $2$.

Determine whether $2745$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2745$ is divisible by $3$.

It is divisible, thus, divide $2745$ by ${\color{green}3}$: $\frac{2745}{3} = {\color{red}915}$.

Determine whether $915$ is divisible by $3$.

It is divisible, thus, divide $915$ by ${\color{green}3}$: $\frac{915}{3} = {\color{red}305}$.

Determine whether $305$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $305$ is divisible by $5$.

It is divisible, thus, divide $305$ by ${\color{green}5}$: $\frac{305}{5} = {\color{red}61}$.

The prime number ${\color{green}61}$ has no other factors then $1$ and ${\color{green}61}$: $\frac{61}{61} = {\color{red}1}$.

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: $2745 = 3^{2} \cdot 5 \cdot 61$.

The prime factorization is $2745 = 3^{2} \cdot 5 \cdot 61$A.