# Prime factorization of $4886$

The calculator will find the prime factorization of $4886$, with steps shown.

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Find the prime factorization of $4886$.

### Solution

Start with the number $2$.

Determine whether $4886$ is divisible by $2$.

It is divisible, thus, divide $4886$ by ${\color{green}2}$: $\frac{4886}{2} = {\color{red}2443}$.

Determine whether $2443$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2443$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2443$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2443$ is divisible by $7$.

It is divisible, thus, divide $2443$ by ${\color{green}7}$: $\frac{2443}{7} = {\color{red}349}$.

The prime number ${\color{green}349}$ has no other factors then $1$ and ${\color{green}349}$: $\frac{349}{349} = {\color{red}1}$.

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: $4886 = 2 \cdot 7 \cdot 349$.

The prime factorization is $4886 = 2 \cdot 7 \cdot 349$A.