# Prime factorization of $744$

The calculator will find the prime factorization of $744$, with steps shown.

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Find the prime factorization of $744$.

### Solution

Start with the number $2$.

Determine whether $744$ is divisible by $2$.

It is divisible, thus, divide $744$ by ${\color{green}2}$: $\frac{744}{2} = {\color{red}372}$.

Determine whether $372$ is divisible by $2$.

It is divisible, thus, divide $372$ by ${\color{green}2}$: $\frac{372}{2} = {\color{red}186}$.

Determine whether $186$ is divisible by $2$.

It is divisible, thus, divide $186$ by ${\color{green}2}$: $\frac{186}{2} = {\color{red}93}$.

Determine whether $93$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $93$ is divisible by $3$.

It is divisible, thus, divide $93$ by ${\color{green}3}$: $\frac{93}{3} = {\color{red}31}$.

The prime number ${\color{green}31}$ has no other factors then $1$ and ${\color{green}31}$: $\frac{31}{31} = {\color{red}1}$.

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: $744 = 2^{3} \cdot 3 \cdot 31$.

The prime factorization is $744 = 2^{3} \cdot 3 \cdot 31$A.