Question

drag each pair of numbers to show if their greatest common factor (gcf) is less than 8, equal to 8, or greater than 8. 24 and 36 16 and 24 12 and 18 3 and 6 12 and 32 2 and 4 gcf is less than 8. drag and drop items here gcf is equal to 8. drag and drop items here gcf is greater than 8 drag and drop items here

Explanation:

To solve this, we calculate the GCF for each pair:

1. Pair: 24 and 36

• Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
• Factors of 36: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)
• Common factors: \(1, 2, 3, 4, 6, 12\)
• GCF: \(12\) (greater than 8)

2. Pair: 16 and 24

• Factors of 16: \(1, 2, 4, 8, 16\)
• Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
• Common factors: \(1, 2, 4, 8\)
• GCF: \(8\) (equal to 8)

3. Pair: 12 and 18

• Factors of 12: \(1, 2, 3, 4, 6, 12\)
• Factors of 18: \(1, 2, 3, 6, 9, 18\)
• Common factors: \(1, 2, 3, 6\)
• GCF: \(6\) (less than 8)

4. Pair: 3 and 6

• Factors of 3: \(1, 3\)
• Factors of 6: \(1, 2, 3, 6\)
• Common factors: \(1, 3\)
• GCF: \(3\) (less than 8)

5. Pair: 12 and 32

• Factors of 12: \(1, 2, 3, 4, 6, 12\)
• Factors of 32: \(1, 2, 4, 8, 16, 32\)
• Common factors: \(1, 2, 4\)
• GCF: \(4\) (less than 8)

6. Pair: 2 and 4

• Factors of 2: \(1, 2\)
• Factors of 4: \(1, 2, 4\)
• Common factors: \(1, 2\)
• GCF: \(2\) (less than 8)

Final Categorization:

• GCF is less than 8: 12 and 18, 3 and 6, 12 and 32, 2 and 4
• GCF is equal to 8: 16 and 24
• GCF is greater than 8: 24 and 36

Answer:

(Drag and Drop):

• Drag "12 and 18", "3 and 6", "12 and 32", "2 and 4" to "GCF is less than 8".
• Drag "16 and 24" to "GCF is equal to 8".
• Drag "24 and 36" to "GCF is greater than 8".