# Prime factorization of $4845$

The calculator will find the prime factorization of $4845$, with steps shown.

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Find the prime factorization of $4845$.

### Solution

Start with the number $2$.

Determine whether $4845$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4845$ is divisible by $3$.

It is divisible, thus, divide $4845$ by ${\color{green}3}$: $\frac{4845}{3} = {\color{red}1615}$.

Determine whether $1615$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1615$ is divisible by $5$.

It is divisible, thus, divide $1615$ by ${\color{green}5}$: $\frac{1615}{5} = {\color{red}323}$.

Determine whether $323$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $323$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $323$ is divisible by $11$.

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

The next prime number is $13$.

Determine whether $323$ is divisible by $13$.

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

The next prime number is $17$.

Determine whether $323$ is divisible by $17$.

It is divisible, thus, divide $323$ by ${\color{green}17}$: $\frac{323}{17} = {\color{red}19}$.

The prime number ${\color{green}19}$ has no other factors then $1$ and ${\color{green}19}$: $\frac{19}{19} = {\color{red}1}$.

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: $4845 = 3 \cdot 5 \cdot 17 \cdot 19$.

The prime factorization is $4845 = 3 \cdot 5 \cdot 17 \cdot 19$A.