# Prime factorization of $3806$

The calculator will find the prime factorization of $3806$, with steps shown.

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Find the prime factorization of $3806$.

### Solution

Start with the number $2$.

Determine whether $3806$ is divisible by $2$.

It is divisible, thus, divide $3806$ by ${\color{green}2}$: $\frac{3806}{2} = {\color{red}1903}$.

Determine whether $1903$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $1903$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $1903$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $1903$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $1903$ is divisible by $11$.

It is divisible, thus, divide $1903$ by ${\color{green}11}$: $\frac{1903}{11} = {\color{red}173}$.

The prime number ${\color{green}173}$ has no other factors then $1$ and ${\color{green}173}$: $\frac{173}{173} = {\color{red}1}$.

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: $3806 = 2 \cdot 11 \cdot 173$.

The prime factorization is $3806 = 2 \cdot 11 \cdot 173$A.