# Prime factorization of $4293$

The calculator will find the prime factorization of $4293$, with steps shown.

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Find the prime factorization of $4293$.

### Solution

Start with the number $2$.

Determine whether $4293$ is divisible by $2$.

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

The next prime number is $3$.

Determine whether $4293$ is divisible by $3$.

It is divisible, thus, divide $4293$ by ${\color{green}3}$: $\frac{4293}{3} = {\color{red}1431}$.

Determine whether $1431$ is divisible by $3$.

It is divisible, thus, divide $1431$ by ${\color{green}3}$: $\frac{1431}{3} = {\color{red}477}$.

Determine whether $477$ is divisible by $3$.

It is divisible, thus, divide $477$ by ${\color{green}3}$: $\frac{477}{3} = {\color{red}159}$.

Determine whether $159$ is divisible by $3$.

It is divisible, thus, divide $159$ by ${\color{green}3}$: $\frac{159}{3} = {\color{red}53}$.

The prime number ${\color{green}53}$ has no other factors then $1$ and ${\color{green}53}$: $\frac{53}{53} = {\color{red}1}$.

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: $4293 = 3^{4} \cdot 53$.

The prime factorization is $4293 = 3^{4} \cdot 53$A.