# Prime factorization of $4032$

The calculator will find the prime factorization of $4032$, with steps shown.

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Find the prime factorization of $4032$.

### Solution

Start with the number $2$.

Determine whether $4032$ is divisible by $2$.

It is divisible, thus, divide $4032$ by ${\color{green}2}$: $\frac{4032}{2} = {\color{red}2016}$.

Determine whether $2016$ is divisible by $2$.

It is divisible, thus, divide $2016$ by ${\color{green}2}$: $\frac{2016}{2} = {\color{red}1008}$.

Determine whether $1008$ is divisible by $2$.

It is divisible, thus, divide $1008$ by ${\color{green}2}$: $\frac{1008}{2} = {\color{red}504}$.

Determine whether $504$ is divisible by $2$.

It is divisible, thus, divide $504$ by ${\color{green}2}$: $\frac{504}{2} = {\color{red}252}$.

Determine whether $252$ is divisible by $2$.

It is divisible, thus, divide $252$ by ${\color{green}2}$: $\frac{252}{2} = {\color{red}126}$.

Determine whether $126$ is divisible by $2$.

It is divisible, thus, divide $126$ by ${\color{green}2}$: $\frac{126}{2} = {\color{red}63}$.

Determine whether $63$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $63$ is divisible by $3$.

It is divisible, thus, divide $63$ by ${\color{green}3}$: $\frac{63}{3} = {\color{red}21}$.

Determine whether $21$ is divisible by $3$.

It is divisible, thus, divide $21$ by ${\color{green}3}$: $\frac{21}{3} = {\color{red}7}$.

The prime number ${\color{green}7}$ has no other factors then $1$ and ${\color{green}7}$: $\frac{7}{7} = {\color{red}1}$.

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: $4032 = 2^{6} \cdot 3^{2} \cdot 7$.

The prime factorization is $4032 = 2^{6} \cdot 3^{2} \cdot 7$A.