# Prime factorization of $4689$

The calculator will find the prime factorization of $4689$, with steps shown.

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Find the prime factorization of $4689$.

### Solution

Start with the number $2$.

Determine whether $4689$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4689$ is divisible by $3$.

It is divisible, thus, divide $4689$ by ${\color{green}3}$: $\frac{4689}{3} = {\color{red}1563}$.

Determine whether $1563$ is divisible by $3$.

It is divisible, thus, divide $1563$ by ${\color{green}3}$: $\frac{1563}{3} = {\color{red}521}$.

The prime number ${\color{green}521}$ has no other factors then $1$ and ${\color{green}521}$: $\frac{521}{521} = {\color{red}1}$.

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: $4689 = 3^{2} \cdot 521$.

The prime factorization is $4689 = 3^{2} \cdot 521$A.