Write down all the composite numbers less than 20.
The correct answer and explanation is:
The composite numbers less than 20 are:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18.
A composite number is a positive integer greater than 1 that has more than two distinct positive divisors. This means that in addition to being divisible by 1 and itself, a composite number is divisible by at least one other number. To distinguish between prime and composite numbers, prime numbers have exactly two distinct positive divisors: 1 and the number itself.
For example:
- 4 is divisible by 1, 2, and 4, making it composite.
- 6 is divisible by 1, 2, 3, and 6, which also makes it composite.
- 8 is divisible by 1, 2, 4, and 8, so it is composite.
- 9 is divisible by 1, 3, and 9, making it composite.
- 10 has divisors 1, 2, 5, and 10, so it is composite.
- 12 is divisible by 1, 2, 3, 4, 6, and 12, indicating that it is composite.
- 14 is divisible by 1, 2, 7, and 14, which classifies it as a composite number.
- 15 has divisors 1, 3, 5, and 15, making it composite.
- 16 is divisible by 1, 2, 4, 8, and 16, so it is composite.
- 18 is divisible by 1, 2, 3, 6, 9, and 18, making it composite.
On the other hand, the numbers 2, 3, 5, 7, 11, 13, 17, and 19 are prime because they only have two divisors: 1 and themselves. Therefore, all numbers that are not prime and greater than 1 are composite.