64, 48 and 16 GCF 48,64 and 32 GCF
The correct answer and explanation is:
Correct Answers:
- GCF of 64, 48, and 16: 16
- GCF of 48, 64, and 32: 16
Explanation (300 words):
The Greatest Common Factor (GCF) is the largest number that can evenly divide each of the numbers in a given set without leaving a remainder. Finding the GCF is helpful in simplifying fractions, solving problems involving ratios, and more.
1. GCF of 64, 48, and 16:
Let’s find the factors of each:
- Factors of 64: 1, 2, 4, 8, 16, 32, 64
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 16: 1, 2, 4, 8, 16
Now, the common factors of all three numbers are:
1, 2, 4, 8, 16
So the greatest one is 16.
2. GCF of 48, 64, and 32:
Let’s find the factors:
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 64: 1, 2, 4, 8, 16, 32, 64
- Factors of 32: 1, 2, 4, 8, 16, 32
Common factors: 1, 2, 4, 8, 16
Greatest one: 16
Optional: Prime Factorization Method
You can also use prime factorization:
- 64 = 2⁶
- 48 = 2⁴ × 3
- 16 = 2⁴
The smallest power of 2 common to all is 2⁴ = 16.
Similarly:
- 48 = 2⁴ × 3
- 64 = 2⁶
- 32 = 2⁵
The lowest power of 2 common to all is again 2⁴ = 16.
Conclusion:
In both cases, the GCF is 16, which is the largest number that evenly divides all numbers in each group. This process helps break down numbers to their simplest shared components.