Answer :
To determine which pairs of numbers have a greatest common factor (GCF) of 6, follow these steps:
1. Understand the Greatest Common Factor (GCF): The GCF of two numbers is the largest number that divides both of them without any remainder.
2. Check Each Pair:
- A. 18 and 24:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 6
- The greatest of these is 6.
- B. 21 and 36:
- Factors of 21: 1, 3, 7, 21
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common factors: 1, 3
- The greatest of these is 3.
- C. 30 and 48:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Common factors: 1, 2, 3, 6
- The greatest of these is 6.
- D. 36 and 60:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Common factors: 1, 2, 3, 4, 6, 12
- The greatest of these is 12.
- E. 48 and 72:
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Common factors: 1, 2, 3, 4, 6, 8, 12, 24
- The greatest of these is 24.
- F. 54 and 84:
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Common factors: 1, 2, 3, 6
- The greatest of these is 6.
3. Conclusion:
Based on the above evaluation, the pairs that have a greatest common factor of 6 are:
- A: 18 and 24
- C: 30 and 48
- F: 54 and 84
Therefore, the correct answers are A, C, and F.
1. Understand the Greatest Common Factor (GCF): The GCF of two numbers is the largest number that divides both of them without any remainder.
2. Check Each Pair:
- A. 18 and 24:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 3, 6
- The greatest of these is 6.
- B. 21 and 36:
- Factors of 21: 1, 3, 7, 21
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common factors: 1, 3
- The greatest of these is 3.
- C. 30 and 48:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Common factors: 1, 2, 3, 6
- The greatest of these is 6.
- D. 36 and 60:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Common factors: 1, 2, 3, 4, 6, 12
- The greatest of these is 12.
- E. 48 and 72:
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Common factors: 1, 2, 3, 4, 6, 8, 12, 24
- The greatest of these is 24.
- F. 54 and 84:
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Common factors: 1, 2, 3, 6
- The greatest of these is 6.
3. Conclusion:
Based on the above evaluation, the pairs that have a greatest common factor of 6 are:
- A: 18 and 24
- C: 30 and 48
- F: 54 and 84
Therefore, the correct answers are A, C, and F.
