what numbers i can use to make in exponents a prime factorization of 198

Answer 1

To perform a prime factorization of the number $198$, we can break it down into its prime factors.

1. Start by dividing $198$ by the smallest prime number, which is $2$: $$198÷2=99$$ Thus, $198=2\times 99$.

2. Next, we factor $99$. The smallest prime that divides $99$ is $3$: $$99÷3=33$$ Therefore, $99=3\times 33$ and we have $198=2\times 3\times 33$.

3. Now, we continue factoring $33$. The smallest prime dividing $33$ is $3$ again: $$33÷3=11$$ So $33=3\times 11$ and we have $198=2\times 3\times 3\times 11$, or $198=2\times 3^2\times 11$.

4. Now, $11$ is a prime number and cannot be factored further.

Therefore, the prime factorization of $198$ is: $$198=2^1\times 3^2\times {11}^1$$

In summary, the prime factors of $198$ are $2$, $3$, and $11$ in exponential form $2^1,3^2,{11}^1$.