# Prime factorization of $4707$

The calculator will find the prime factorization of $4707$, with steps shown.

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Find the prime factorization of $4707$.

### Solution

Start with the number $2$.

Determine whether $4707$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4707$ is divisible by $3$.

It is divisible, thus, divide $4707$ by ${\color{green}3}$: $\frac{4707}{3} = {\color{red}1569}$.

Determine whether $1569$ is divisible by $3$.

It is divisible, thus, divide $1569$ by ${\color{green}3}$: $\frac{1569}{3} = {\color{red}523}$.

The prime number ${\color{green}523}$ has no other factors then $1$ and ${\color{green}523}$: $\frac{523}{523} = {\color{red}1}$.

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: $4707 = 3^{2} \cdot 523$.

The prime factorization is $4707 = 3^{2} \cdot 523$A.