greatest common factor of 56 and 96
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 56 and 96. To solve this, we will identify the factors of both numbers and find the largest factor that they share.
Answer
The greatest common factor (GCF) of 56 and 96 is $8$.
Answer for screen readers
The greatest common factor (GCF) of 56 and 96 is $8$.
Steps to Solve
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List the factors of each number
First, we need to identify all the factors of 56 and 96.
Factors of 56:
- Start with 1 and 56 (1 × 56 = 56)
- Next, 2 and 28 (2 × 28 = 56)
- Then, 4 and 14 (4 × 14 = 56)
- Finally, 7 and 8 (7 × 8 = 56)
So, the factors of 56 are: $1, 2, 4, 7, 8, 14, 28, 56$.
Factors of 96:
- Start with 1 and 96 (1 × 96 = 96)
- Next, 2 and 48 (2 × 48 = 96)
- Then, 3 and 32 (3 × 32 = 96)
- After that, 4 and 24 (4 × 24 = 96)
- Next, 6 and 16 (6 × 16 = 96)
- Finally, 8 and 12 (8 × 12 = 96)
So, the factors of 96 are: $1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96$.
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Identify common factors
Next, we find the factors that are common to both 56 and 96.
The common factors are: $1, 2, 4, 8$.
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Determine the greatest common factor (GCF)
Now, we pick the largest common factor from the list. The largest number among the common factors $1, 2, 4, 8$ is $8$.
Thus, the greatest common factor (GCF) of 56 and 96 is $8$.
The greatest common factor (GCF) of 56 and 96 is $8$.
More Information
Finding the GCF helps simplify fractions and is useful in various areas of mathematics, including number theory. The GCF is the largest number that divides both given numbers without leaving a remainder.
Tips
- Failing to list all the factors correctly may lead to missing the greatest common factor.
- Not checking all common factors could cause one to overlook the largest one.
