Which of the following is a composite number?
27 is a composite number.
A composite number is defined as a positive integer that has at least one divisor other than 1 and itself. Since 27 can be factored into 3 x 9, it meets this criterion, distinguishing it from prime numbers, which have only two divisors.
7 is a prime number because it has no divisors other than 1 and itself. The only factors of 7 are 1 and 7, meaning it cannot be classified as a composite number since it does not meet the definition of having additional divisors.
Similar to 7, 17 is also a prime number. It has no divisors other than 1 and 17, confirming that it does not qualify as a composite number. Prime numbers are characterized by having exactly two distinct positive divisors.
27 is a composite number because it can be expressed as the product of 3 multiplied by 9. Additionally, it has other divisors, including 1, 3, 9, and 27, which confirms its classification as composite due to having more than two positive divisors.
37 is a prime number as well, possessing only two divisors: 1 and 37. It cannot be expressed as a product of two smaller positive integers, thus excluding it from being classified as a composite number.
In summary, composite numbers are defined by their multiple divisors, while prime numbers have only two. Among the choices provided, 27 stands out as a composite number, being divisible by factors other than 1 and itself. The other options—7, 17, and 37—are all prime, reinforcing the distinction between these two types of integers.
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