What is the greatest common factor of 56 and 42?
Understand the Problem
The question is asking for the greatest common factor (GCF), also known as the greatest common divisor (GCD), of the numbers 56 and 42. To find this, we will identify the factors of both numbers and determine which factor is the largest that they share.
Answer
The greatest common factor of 56 and 42 is \( 14 \).
Answer for screen readers
The greatest common factor (GCF) of 56 and 42 is ( 14 ).
Steps to Solve
- List the factors of each number
First, we will find all the factors of the numbers 56 and 42.
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Identify common factors
Now, we need to find the factors that are common to both lists.
Common factors are: 1, 2, 7, 14
- Determine the greatest common factor
Among the common factors identified, we need to find the largest one.
The greatest common factor is 14.
The greatest common factor (GCF) of 56 and 42 is ( 14 ).
More Information
The GCF is useful in simplifying fractions, finding common denominators, and solving problems involving ratios. It represents the largest number that divides both numbers without leaving a remainder.
Tips
- Failing to list all factors correctly. To avoid this, ensure you check divisibility for each number thoroughly.
- Confusing GCF with LCM (Least Common Multiple). Remember that GCF is the largest common factor, while LCM is the smallest.
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