product of prime factors 99
Understand the Problem
The question is asking for the prime factorization of the number 99, specifically looking for the product of its prime factors.
Answer
The prime factorization of 99 is $3^2 \times 11$.
Answer for screen readers
The prime factorization of 99 is $3^2 \times 11$.
Steps to Solve
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Divide by the smallest prime number Start by checking the smallest prime number, which is 2. Since 99 is odd, it cannot be divided by 2.
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Check the next smallest prime number Next, check the prime number 3. Divide 99 by 3:
$$ 99 \div 3 = 33 $$
- Continue factoring 33 Now we need to factor 33. Again, check 3:
$$ 33 \div 3 = 11 $$
- Identify the final prime factor At this point, we have factored 99 down to 11, which is itself a prime number. Therefore, the complete factorization of 99 is:
$$ 99 = 3 \times 3 \times 11 $$
- Express with prime factorization Since we have two 3's, we can also express the prime factorization as:
$$ 99 = 3^2 \times 11 $$
The prime factorization of 99 is $3^2 \times 11$.
More Information
Prime factorization is useful in various fields of mathematics, including number theory. Understanding how to break down numbers into their prime factors can help in simplifying fractions and finding the least common multiples or greatest common divisors.
Tips
- A common mistake is failing to check all prime numbers sequentially. It's important to divide by the smallest primes first.
- Confusing prime factors with composite factors, which can lead to incorrect results. Remember, only prime numbers are considered in the prime factorization.
