Find the greatest common factors of the following numbers. 1. 28 32 4) 12 16 20 2. 12 30 48 5) 8 56 80 112 3. 20 32 40
The Correct Answer and Explanation is:
Let’s break down the greatest common factors (GCF) for each set of numbers.
1. 28, 32, 4
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 4: 1, 2, 4
The greatest common factor for 28, 32, and 4 is 4 because it is the largest number that divides all three numbers.
2. 12, 30, 48
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The greatest common factor for 12, 30, and 48 is 6, as it’s the largest number that divides all three numbers.
3. 20, 32, 40
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The greatest common factor for 20, 32, and 40 is 4, as it is the largest factor common to all three numbers.
4. 12, 16, 20
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 16: 1, 2, 4, 8, 16
- Factors of 20: 1, 2, 4, 5, 10, 20
The greatest common factor for 12, 16, and 20 is 4, as it’s the largest number that divides all three numbers.
5. 8, 56, 80, 112
- Factors of 8: 1, 2, 4, 8
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The greatest common factor for 8, 56, 80, and 112 is 8, as it is the largest number that divides all four numbers.
Conclusion:
- GCF of 28, 32, 4 = 4
- GCF of 12, 30, 48 = 6
- GCF of 20, 32, 40 = 4
- GCF of 12, 16, 20 = 4
- GCF of 8, 56, 80, 112 = 8
The GCF is the largest number that divides evenly into all the numbers in the set, and finding it requires identifying all factors and selecting the highest common factor.
