# Prime factorization of $4136$

The calculator will find the prime factorization of $4136$, with steps shown.

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Find the prime factorization of $4136$.

### Solution

Start with the number $2$.

Determine whether $4136$ is divisible by $2$.

It is divisible, thus, divide $4136$ by ${\color{green}2}$: $\frac{4136}{2} = {\color{red}2068}$.

Determine whether $2068$ is divisible by $2$.

It is divisible, thus, divide $2068$ by ${\color{green}2}$: $\frac{2068}{2} = {\color{red}1034}$.

Determine whether $1034$ is divisible by $2$.

It is divisible, thus, divide $1034$ by ${\color{green}2}$: $\frac{1034}{2} = {\color{red}517}$.

Determine whether $517$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $517$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $517$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $517$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $517$ is divisible by $11$.

It is divisible, thus, divide $517$ by ${\color{green}11}$: $\frac{517}{11} = {\color{red}47}$.

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: $4136 = 2^{3} \cdot 11 \cdot 47$.

The prime factorization is $4136 = 2^{3} \cdot 11 \cdot 47$A.