1. Which of the following is a composite number?
Answer: C
27 is a composite number.
A composite number is defined as a positive integer that has at least one positive divisor other than one or itself. In this case, 27 has multiple divisors, which makes it a composite number.
A) 7
7 is a prime number because it has exactly two distinct positive divisors: 1 and 7 itself. Therefore, it does not meet the criteria for being a composite number.
B) 17
17 is also a prime number, as it has only two positive divisors: 1 and 17. This disqualifies it from being classified as a composite number.
C) 27
27 is a composite number because it has divisors other than 1 and itself. Specifically, it can be divided by 1, 3, 9, and 27, indicating that it has more than two factors.
D) 37
37 is a prime number because it only has two positive divisors: 1 and 37. Thus, it cannot be considered a composite number.
Conclusion
27 is definitively a composite number due to its multiple divisors, while all other options (7, 17, and 37) are prime numbers with only two distinct divisors. This highlights the fundamental difference between prime and composite numbers, reinforcing the definition that composite numbers must have factors beyond just one and themselves.