# Prime factorization of $4020$

The calculator will find the prime factorization of $4020$, with steps shown.

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Find the prime factorization of $4020$.

### Solution

Start with the number $2$.

Determine whether $4020$ is divisible by $2$.

It is divisible, thus, divide $4020$ by ${\color{green}2}$: $\frac{4020}{2} = {\color{red}2010}$.

Determine whether $2010$ is divisible by $2$.

It is divisible, thus, divide $2010$ by ${\color{green}2}$: $\frac{2010}{2} = {\color{red}1005}$.

Determine whether $1005$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1005$ is divisible by $3$.

It is divisible, thus, divide $1005$ by ${\color{green}3}$: $\frac{1005}{3} = {\color{red}335}$.

Determine whether $335$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $335$ is divisible by $5$.

It is divisible, thus, divide $335$ by ${\color{green}5}$: $\frac{335}{5} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$.

The prime factorization is $4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67$A.