# Prime factorization of $4606$

The calculator will find the prime factorization of $4606$, with steps shown.

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Find the prime factorization of $4606$.

### Solution

Start with the number $2$.

Determine whether $4606$ is divisible by $2$.

It is divisible, thus, divide $4606$ by ${\color{green}2}$: $\frac{4606}{2} = {\color{red}2303}$.

Determine whether $2303$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $2303$ is divisible by $3$.

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

The next prime number is $5$.

Determine whether $2303$ is divisible by $5$.

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

The next prime number is $7$.

Determine whether $2303$ is divisible by $7$.

It is divisible, thus, divide $2303$ by ${\color{green}7}$: $\frac{2303}{7} = {\color{red}329}$.

Determine whether $329$ is divisible by $7$.

It is divisible, thus, divide $329$ by ${\color{green}7}$: $\frac{329}{7} = {\color{red}47}$.

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: $4606 = 2 \cdot 7^{2} \cdot 47$.

The prime factorization is $4606 = 2 \cdot 7^{2} \cdot 47$A.