What is the greatest common factor of 56 and 72?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 56 and 72. We will find the GCF by determining the factors of both numbers and identifying the largest factor that they have in common.
Answer
The GCF of 56 and 72 is $8$.
Answer for screen readers
The greatest common factor (GCF) of 56 and 72 is $8$.
Steps to Solve
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Determine the factors of 56 Start by listing all the factors of 56. A factor is a number that divides 56 without leaving a remainder. The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56.
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Determine the factors of 72 Next, list all the factors of 72. The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
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Identify common factors Now, look for numbers that appear in both lists of factors. The common factors of 56 and 72 are: 1, 2, 4, 8.
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Find the greatest common factor Finally, from the list of common factors, identify the greatest one. The greatest common factor (GCF) is 8.
The greatest common factor (GCF) of 56 and 72 is $8$.
More Information
The GCF is important in various mathematical applications, such as simplifying fractions or finding common denominators. It helps to understand the relationship between numbers and can be applied in various mathematical contexts.
Tips
- Missing factors: Sometimes, people forget to list all the factors, leading to an incorrect GCF. Always ensure to include all potential factors.
- Not identifying common factors properly: It's essential to compare both lists carefully to identify all shared factors correctly.
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