# Prime factorization of $3948$

The calculator will find the prime factorization of $3948$, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the prime factorization of $3948$.

### Solution

Start with the number $2$.

Determine whether $3948$ is divisible by $2$.

It is divisible, thus, divide $3948$ by ${\color{green}2}$: $\frac{3948}{2} = {\color{red}1974}$.

Determine whether $1974$ is divisible by $2$.

It is divisible, thus, divide $1974$ by ${\color{green}2}$: $\frac{1974}{2} = {\color{red}987}$.

Determine whether $987$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $987$ is divisible by $3$.

It is divisible, thus, divide $987$ by ${\color{green}3}$: $\frac{987}{3} = {\color{red}329}$.

Determine whether $329$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $329$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $329$ is divisible by $7$.

It is divisible, thus, divide $329$ by ${\color{green}7}$: $\frac{329}{7} = {\color{red}47}$.

The prime number ${\color{green}47}$ has no other factors then $1$ and ${\color{green}47}$: $\frac{47}{47} = {\color{red}1}$.

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: $3948 = 2^{2} \cdot 3 \cdot 7 \cdot 47$.

The prime factorization is $3948 = 2^{2} \cdot 3 \cdot 7 \cdot 47$A.