Which of the following numbers are prime numbers? 2, 12, 17, 19, 24, 37, 42, 48, 51, 57, 97, 99, 100. Which are composite numbers: 29, 35, 37, 42, 48, 51, 66, 87, 99, 100.
The Correct Answer and Explanation is:
Prime Numbers:
A prime number is a whole number greater than 1 that has no positive divisors other than 1 and itself. Let’s check each number:
- 2: Prime. The only even prime number, divisible only by 1 and 2.
- 12: Not prime. Divisible by 1, 2, 3, 4, 6, and 12.
- 17: Prime. Divisible only by 1 and 17.
- 19: Prime. Divisible only by 1 and 19.
- 24: Not prime. Divisible by 1, 2, 3, 4, 6, 8, 12, and 24.
- 37: Prime. Divisible only by 1 and 37.
- 42: Not prime. Divisible by 1, 2, 3, 6, 7, 14, 21, and 42.
- 48: Not prime. Divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
- 51: Not prime. Divisible by 1, 3, 17, and 51.
- 57: Not prime. Divisible by 1, 3, 19, and 57.
- 97: Prime. Divisible only by 1 and 97.
- 99: Not prime. Divisible by 1, 3, 9, 11, 33, and 99.
- 100: Not prime. Divisible by 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Composite Numbers:
A composite number is a whole number greater than 1 that has divisors other than 1 and itself. Let’s check each number:
- 29: Not composite. It’s a prime number.
- 35: Composite. Divisible by 1, 5, 7, and 35.
- 37: Not composite. It’s a prime number.
- 42: Composite. Divisible by 1, 2, 3, 6, 7, 14, 21, and 42.
- 48: Composite. Divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
- 51: Composite. Divisible by 1, 3, 17, and 51.
- 66: Composite. Divisible by 1, 2, 3, 6, 11, 22, 33, and 66.
- 87: Composite. Divisible by 1, 3, 29, and 87.
- 99: Composite. Divisible by 1, 3, 9, 11, 33, and 99.
- 100: Composite. Divisible by 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Summary:
- Prime Numbers: 2, 17, 19, 37, 97
- Composite Numbers: 35, 42, 48, 51, 66, 87, 99, 100
Prime numbers are indivisible except by 1 and themselves, while composite numbers have more divisors.
