Question

drag each description to the correct number. each number will have two descriptions.
descriptions: has exactly 2 factors, composite, neither prime nor composite, has less than 2 factors, has more than 2 factors, prime
numbers: 71 (two descriptions), 8 (two descriptions), 1 (two descriptions)
drag and drop items here (for 71), drag and drop items here (for 8), drag and drop items here (for 1)

Explanation:

Step1: Analyze 71

A prime number is defined as a number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Let's check the factors of 71. We test divisibility: 71 is not divisible by 2 (since it's odd), not by 3 (7+1=8, not divisible by 3), not by 5 (doesn't end in 0 or 5), 710=70, 71/7≈10.14, 116=66, 11*7=77>71. So the only factors are 1 and 71. So 71 is prime and has exactly 2 factors.

Step2: Analyze 8

A composite number is a positive integer that has at least one positive divisor other than one or itself. The factors of 8 are 1, 2, 4, 8. So it has more than 2 factors (specifically 4 factors) and is composite.

Step3: Analyze 1

By definition, 1 is neither prime nor composite. A prime number must have exactly two distinct factors, but 1 has only one factor (itself). A composite number must have more than two factors, which 1 does not. So 1 has less than 2 factors (only 1 factor) and is neither prime nor composite.

Answer:

• For 71: Drag "Prime" and "Has Exactly 2 Factors" to its drop area.
• For 8: Drag "Composite" and "Has More Than 2 Factors" to its drop area.
• For 1: Drag "Neither Prime Nor Composite" and "Has Less Than 2 Factors" to its drop area.