Question

Is 42 prime or composite? How did you know?

A) Prime - because it has only two distinct positive divisors: 1 and 42
B) Composite - because it has more than two distinct positive divisors
C) Prime - because it is an even number
D) Composite - because it is an odd number

Answer 1

The number 42 is composite because it has multiple divisors beyond just 1 and itself. It can be divided by 2, making it evidently a composite number, since the only even prime number is 2.

Step-by-step explanation:

The number 42 is composite because it has more than two distinct positive divisors. By definition, a prime number has only two distinct positive divisors, 1 and itself. On the other hand, a composite number has additional divisors apart from 1 and itself. In the case of 42, it can be divided by 1, 2, 3, 6, 7, 14, 21, and 42. Since 42 is divisible by numbers other than 1 and itself, the correct answer is B) Composite - because it has more than two distinct positive divisors.

Knowing whether a number is prime or composite usually involves checking its divisibility by numbers smaller than itself. For even numbers, which are multiples of 2, it is straightforward to know that they are composite, except for the number 2, which is the only even prime number. Since 42 is even and greater than 2, it is immediately clear that it is composite.