# Prime factorization of $3048$

The calculator will find the prime factorization of $3048$, with steps shown.

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Find the prime factorization of $3048$.

### Solution

Start with the number $2$.

Determine whether $3048$ is divisible by $2$.

It is divisible, thus, divide $3048$ by ${\color{green}2}$: $\frac{3048}{2} = {\color{red}1524}$.

Determine whether $1524$ is divisible by $2$.

It is divisible, thus, divide $1524$ by ${\color{green}2}$: $\frac{1524}{2} = {\color{red}762}$.

Determine whether $762$ is divisible by $2$.

It is divisible, thus, divide $762$ by ${\color{green}2}$: $\frac{762}{2} = {\color{red}381}$.

Determine whether $381$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $381$ is divisible by $3$.

It is divisible, thus, divide $381$ by ${\color{green}3}$: $\frac{381}{3} = {\color{red}127}$.

The prime number ${\color{green}127}$ has no other factors then $1$ and ${\color{green}127}$: $\frac{127}{127} = {\color{red}1}$.

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: $3048 = 2^{3} \cdot 3 \cdot 127$.

The prime factorization is $3048 = 2^{3} \cdot 3 \cdot 127$A.