which of the following number are prime or composite or 99 91
The correct answer and explanation is:
Answer:
- 99 is a composite number.
- 91 is a composite number.
Explanation:
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. This means it cannot be divided evenly by any other number. On the other hand, a composite number has more than two factors — it can be divided by numbers other than 1 and itself.
Let’s evaluate the numbers:
99
To check if 99 is a prime number, try dividing it by smaller prime numbers:
- 99 ÷ 2 = 49.5 (not divisible)
- 99 ÷ 3 = 33 (divisible)
- 99 ÷ 11 = 9 (divisible)
Since 99 has factors such as 3, 9, 11, and 33, it is not prime. It is composite because it has more than two factors: 1, 3, 9, 11, 33, and 99.
91
Next, test 91 by dividing it by smaller primes:
- 91 ÷ 2 = 45.5 (not divisible)
- 91 ÷ 3 = 30.33 (not divisible)
- 91 ÷ 5 = 18.2 (not divisible)
- 91 ÷ 7 = 13 (divisible)
Since 91 ÷ 7 = 13, and both 7 and 13 are factors of 91, it is not prime. It is composite because it can be divided evenly by numbers other than 1 and itself.
Conclusion
Both 99 and 91 are composite numbers. They are not prime because they have more than two factors. Recognizing whether a number is prime or composite helps in simplifying fractions, finding greatest common divisors, and performing prime factorization, which are useful in many areas of mathematics.