# Prime factorization of $444$

The calculator will find the prime factorization of $444$, with steps shown.

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Find the prime factorization of $444$.

### Solution

Start with the number $2$.

Determine whether $444$ is divisible by $2$.

It is divisible, thus, divide $444$ by ${\color{green}2}$: $\frac{444}{2} = {\color{red}222}$.

Determine whether $222$ is divisible by $2$.

It is divisible, thus, divide $222$ by ${\color{green}2}$: $\frac{222}{2} = {\color{red}111}$.

Determine whether $111$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $111$ is divisible by $3$.

It is divisible, thus, divide $111$ by ${\color{green}3}$: $\frac{111}{3} = {\color{red}37}$.

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: $444 = 2^{2} \cdot 3 \cdot 37$.

The prime factorization is $444 = 2^{2} \cdot 3 \cdot 37$A.