greatest common factor of 55 and 77
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 55 and 77. To find this, we will need to determine the factors of both numbers and identify the largest factor they share.
Answer
The greatest common factor of 55 and 77 is $11$.
Answer for screen readers
The greatest common factor (GCF) of 55 and 77 is $11$.
Steps to Solve
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List the factors of each number Start by finding all the factors of 55. The factors of 55 are 1, 5, 11, and 55. Next, find the factors of 77. The factors of 77 are 1, 7, 11, and 77.
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Identify common factors Now, look for the factors that both 55 and 77 share. The common factors from the lists are 1 and 11.
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Determine the greatest common factor The greatest common factor (GCF) is the largest of the common factors. In this case, the largest common factor between 55 and 77 is 11.
The greatest common factor (GCF) of 55 and 77 is $11$.
More Information
The GCF is useful in simplifying fractions and solving problems that involve divisibility. Knowing how to find the GCF can also help in various applications of algebra and number theory.
Tips
- Misidentifying factors: Make sure to check all numbers up to the number itself to avoid missing any factors.
- Confusing the GCF with the least common multiple (LCM): Remember, the GCF is the largest factor shared, whereas the LCM is the smallest multiple shared.
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