# Prime factorization of $4440$

The calculator will find the prime factorization of $4440$, with steps shown.

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Find the prime factorization of $4440$.

### Solution

Start with the number $2$.

Determine whether $4440$ is divisible by $2$.

It is divisible, thus, divide $4440$ by ${\color{green}2}$: $\frac{4440}{2} = {\color{red}2220}$.

Determine whether $2220$ is divisible by $2$.

It is divisible, thus, divide $2220$ by ${\color{green}2}$: $\frac{2220}{2} = {\color{red}1110}$.

Determine whether $1110$ is divisible by $2$.

It is divisible, thus, divide $1110$ by ${\color{green}2}$: $\frac{1110}{2} = {\color{red}555}$.

Determine whether $555$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $555$ is divisible by $3$.

It is divisible, thus, divide $555$ by ${\color{green}3}$: $\frac{555}{3} = {\color{red}185}$.

Determine whether $185$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $185$ is divisible by $5$.

It is divisible, thus, divide $185$ by ${\color{green}5}$: $\frac{185}{5} = {\color{red}37}$.

The prime number ${\color{green}37}$ has no other factors then $1$ and ${\color{green}37}$: $\frac{37}{37} = {\color{red}1}$.

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: $4440 = 2^{3} \cdot 3 \cdot 5 \cdot 37$.

The prime factorization is $4440 = 2^{3} \cdot 3 \cdot 5 \cdot 37$A.