# Prime factorization of $3752$

The calculator will find the prime factorization of $3752$, 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 $3752$.

### Solution

Start with the number $2$.

Determine whether $3752$ is divisible by $2$.

It is divisible, thus, divide $3752$ by ${\color{green}2}$: $\frac{3752}{2} = {\color{red}1876}$.

Determine whether $1876$ is divisible by $2$.

It is divisible, thus, divide $1876$ by ${\color{green}2}$: $\frac{1876}{2} = {\color{red}938}$.

Determine whether $938$ is divisible by $2$.

It is divisible, thus, divide $938$ by ${\color{green}2}$: $\frac{938}{2} = {\color{red}469}$.

Determine whether $469$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $469$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $469$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $469$ is divisible by $7$.

It is divisible, thus, divide $469$ by ${\color{green}7}$: $\frac{469}{7} = {\color{red}67}$.

The prime number ${\color{green}67}$ has no other factors then $1$ and ${\color{green}67}$: $\frac{67}{67} = {\color{red}1}$.

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: $3752 = 2^{3} \cdot 7 \cdot 67$.

The prime factorization is $3752 = 2^{3} \cdot 7 \cdot 67$A.