# Prime factorization of $4671$

The calculator will find the prime factorization of $4671$, with steps shown.

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Find the prime factorization of $4671$.

### Solution

Start with the number $2$.

Determine whether $4671$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4671$ is divisible by $3$.

It is divisible, thus, divide $4671$ by ${\color{green}3}$: $\frac{4671}{3} = {\color{red}1557}$.

Determine whether $1557$ is divisible by $3$.

It is divisible, thus, divide $1557$ by ${\color{green}3}$: $\frac{1557}{3} = {\color{red}519}$.

Determine whether $519$ is divisible by $3$.

It is divisible, thus, divide $519$ by ${\color{green}3}$: $\frac{519}{3} = {\color{red}173}$.

The prime number ${\color{green}173}$ has no other factors then $1$ and ${\color{green}173}$: $\frac{173}{173} = {\color{red}1}$.

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: $4671 = 3^{3} \cdot 173$.

The prime factorization is $4671 = 3^{3} \cdot 173$A.