How do you know that the product of any two numbers greater than 1 must be a composite number?

Because each of the two numbers is a factor of the product, and since the product has at least those two factors, it's a composite number by definition.

Answered by AL2006 | 2024-06-10

. . . the definition of a composite number is that it is the product of two or more numbers (not including 1 and the number itself) . . . that's what makes it composite . . . so that's how I know . . .

Answered by Anonymous | 2024-06-10

The product of any two numbers greater than 1 is a composite number because it has at least four distinct positive divisors: 1, the two numbers themselves, and the product. For example, multiplying 2 and 3 gives 6, which is composite, as it can be divided by 1, 2, 3, and 6. Thus, any product of two numbers greater than 1 will always have more than two distinct factors, confirming it as composite.
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Answered by AL2006 | 2024-09-04