# Prime factorization of $4686$

The calculator will find the prime factorization of $4686$, with steps shown.

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Find the prime factorization of $4686$.

### Solution

Start with the number $2$.

Determine whether $4686$ is divisible by $2$.

It is divisible, thus, divide $4686$ by ${\color{green}2}$: $\frac{4686}{2} = {\color{red}2343}$.

Determine whether $2343$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2343$ is divisible by $3$.

It is divisible, thus, divide $2343$ by ${\color{green}3}$: $\frac{2343}{3} = {\color{red}781}$.

Determine whether $781$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $781$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $781$ is divisible by $7$.

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

The next prime number is $11$.

Determine whether $781$ is divisible by $11$.

It is divisible, thus, divide $781$ by ${\color{green}11}$: $\frac{781}{11} = {\color{red}71}$.

The prime number ${\color{green}71}$ has no other factors then $1$ and ${\color{green}71}$: $\frac{71}{71} = {\color{red}1}$.

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: $4686 = 2 \cdot 3 \cdot 11 \cdot 71$.

The prime factorization is $4686 = 2 \cdot 3 \cdot 11 \cdot 71$A.