# Prime factorization of $2040$

The calculator will find the prime factorization of $2040$, with steps shown.

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Find the prime factorization of $2040$.

### Solution

Start with the number $2$.

Determine whether $2040$ is divisible by $2$.

It is divisible, thus, divide $2040$ by ${\color{green}2}$: $\frac{2040}{2} = {\color{red}1020}$.

Determine whether $1020$ is divisible by $2$.

It is divisible, thus, divide $1020$ by ${\color{green}2}$: $\frac{1020}{2} = {\color{red}510}$.

Determine whether $510$ is divisible by $2$.

It is divisible, thus, divide $510$ by ${\color{green}2}$: $\frac{510}{2} = {\color{red}255}$.

Determine whether $255$ is divisible by $2$.

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

The next prime number is $3$.

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: $2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17$.

The prime factorization is $2040 = 2^{3} \cdot 3 \cdot 5 \cdot 17$A.