Question

drag each pair of numbers to show if their greatest common factor (gcf) is less than 5, equal to 5, or greater than 5. 12 and 30, 3 and 20, 15 and 20, 20 and 30, 25 and 30, 6 and 33. gcf is less than 5. gcf is equal to 5. gcf is greater than 5. drag and drop items here, drag and drop items here, drag and drop items here

Explanation:

Step1: Find GCF of 12 and 30

Factors of 12: \(1, 2, 3, 4, 6, 12\)
Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
Common factors: \(1, 2, 3, 6\)
GCF: \(6\) (greater than 5)

Step2: Find GCF of 3 and 20

Factors of 3: \(1, 3\)
Factors of 20: \(1, 2, 4, 5, 10, 20\)
Common factors: \(1\)
GCF: \(1\) (less than 5)

Step3: Find GCF of 15 and 20

Factors of 15: \(1, 3, 5, 15\)
Factors of 20: \(1, 2, 4, 5, 10, 20\)
Common factors: \(1, 5\)
GCF: \(5\) (equal to 5)

Step4: Find GCF of 20 and 30

Factors of 20: \(1, 2, 4, 5, 10, 20\)
Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
Common factors: \(1, 2, 5, 10\)
GCF: \(10\) (greater than 5)

Step5: Find GCF of 25 and 30

Factors of 25: \(1, 5, 25\)
Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
Common factors: \(1, 5\)
GCF: \(5\) (equal to 5)

Step6: Find GCF of 6 and 33

Factors of 6: \(1, 2, 3, 6\)
Factors of 33: \(1, 3, 11, 33\)
Common factors: \(1, 3\)
GCF: \(3\) (less than 5)

Categorization:

• GCF < 5: 3 and 20, 6 and 33
• GCF = 5: 15 and 20, 25 and 30
• GCF > 5: 12 and 30, 20 and 30

(To complete the drag-and-drop:

• Drag "3 and 20", "6 and 33" to "GCF is less than 5".
• Drag "15 and 20", "25 and 30" to "GCF is equal to 5".
• Drag "12 and 30", "20 and 30" to "GCF is greater than 5".)

Answer:

Step1: Find GCF of 12 and 30

Factors of 12: \(1, 2, 3, 4, 6, 12\)
Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
Common factors: \(1, 2, 3, 6\)
GCF: \(6\) (greater than 5)

Step2: Find GCF of 3 and 20

Factors of 3: \(1, 3\)
Factors of 20: \(1, 2, 4, 5, 10, 20\)
Common factors: \(1\)
GCF: \(1\) (less than 5)

Step3: Find GCF of 15 and 20

Factors of 15: \(1, 3, 5, 15\)
Factors of 20: \(1, 2, 4, 5, 10, 20\)
Common factors: \(1, 5\)
GCF: \(5\) (equal to 5)

Step4: Find GCF of 20 and 30

Factors of 20: \(1, 2, 4, 5, 10, 20\)
Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
Common factors: \(1, 2, 5, 10\)
GCF: \(10\) (greater than 5)

Step5: Find GCF of 25 and 30

Factors of 25: \(1, 5, 25\)
Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
Common factors: \(1, 5\)
GCF: \(5\) (equal to 5)

Step6: Find GCF of 6 and 33

Factors of 6: \(1, 2, 3, 6\)
Factors of 33: \(1, 3, 11, 33\)
Common factors: \(1, 3\)
GCF: \(3\) (less than 5)

Categorization:

• GCF < 5: 3 and 20, 6 and 33
• GCF = 5: 15 and 20, 25 and 30
• GCF > 5: 12 and 30, 20 and 30

(To complete the drag-and-drop:

• Drag "3 and 20", "6 and 33" to "GCF is less than 5".
• Drag "15 and 20", "25 and 30" to "GCF is equal to 5".
• Drag "12 and 30", "20 and 30" to "GCF is greater than 5".)