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Answer
99 can be written as \( 3 \times 3 \times 11 \) or \( 3^2 \times 11 \).
Solution
To express 99 as a product of its prime factors, we can follow these steps:
1. Start by dividing 99 by the smallest prime number, which is 2. Since 99 is odd, it is not divisible by 2.
2. Next, try dividing by the next smallest prime number, which is 3.
\[
99 \div 3 = 33
\]
So, we can write:
\[
99 = 3 \times 33
\]
3. Now, we need to factor 33. Again, we start with the smallest prime number, which is 2. Since 33 is odd, it is not divisible by 2.
4. Next, we try dividing by 3:
\[
33 \div 3 = 11
\]
So, we can write:
\[
33 = 3 \times 11
\]
5. Now we can substitute back into our equation for 99:
\[
99 = 3 \times (3 \times 11) = 3^2 \times 11
\]
6. Finally, we check if 11 is a prime number. Since it has no divisors other than 1 and itself, it is indeed a prime number.
Thus, the prime factorization of 99 is:
\[
99 = 3^2 \times 11
\]
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Simplify this solution Mind Expander
To express 99 as a product of prime factors, we start by dividing it by the smallest prime number, which is 3. 99 ÷ 3 = 33 Next, we can factor 33 by dividing it by 3 again: 33 ÷ 3 = 11 Now we have reached 11, which is also a prime number. Therefore, the prime factorization of 99 is: 3 × 3 × 11, or written with exponents, 3² × 11. So, 99 can be expressed as the product of its prime factors: **3² × 11**.
