# Prime factorization of $3060$

The calculator will find the prime factorization of $3060$, with steps shown.

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Find the prime factorization of $3060$.

### Solution

Start with the number $2$.

Determine whether $3060$ is divisible by $2$.

It is divisible, thus, divide $3060$ by ${\color{green}2}$: $\frac{3060}{2} = {\color{red}1530}$.

Determine whether $1530$ is divisible by $2$.

It is divisible, thus, divide $1530$ by ${\color{green}2}$: $\frac{1530}{2} = {\color{red}765}$.

Determine whether $765$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $765$ is divisible by $3$.

It is divisible, thus, divide $765$ by ${\color{green}3}$: $\frac{765}{3} = {\color{red}255}$.

Determine whether $255$ is divisible by $3$.

It is divisible, thus, divide $255$ by ${\color{green}3}$: $\frac{255}{3} = {\color{red}85}$.

Determine whether $85$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $85$ is divisible by $5$.

It is divisible, thus, divide $85$ by ${\color{green}5}$: $\frac{85}{5} = {\color{red}17}$.

The prime number ${\color{green}17}$ has no other factors then $1$ and ${\color{green}17}$: $\frac{17}{17} = {\color{red}1}$.

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: $3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17$.

The prime factorization is $3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17$A.