What is the GCF of 80 and 20?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 80 and 20. We will find the factors of each number and identify the highest one they have in common.
Answer
$20$
Answer for screen readers
The greatest common factor (GCF) of 80 and 20 is $20$.
Steps to Solve
- List Factors of Each Number
First, we need to find all the factors of 80. The factors are the numbers that divide 80 without leaving a remainder.
For 80, the factors are:
- 1
- 2
- 4
- 5
- 8
- 10
- 16
- 20
- 40
- 80
Now we find the factors of 20:
- 1
- 2
- 4
- 5
- 10
- 20
- Identify Common Factors
Next, we look for common factors from both lists. The common factors are the numbers that appear in both lists of factors.
The common factors of 80 and 20 are:
- 1
- 2
- 4
- 5
- 10
- 20
- Determine the Greatest Common Factor
Finally, we need to identify the greatest (largest) number from the common factors we found:
The greatest common factor is 20.
The greatest common factor (GCF) of 80 and 20 is $20$.
More Information
Finding the GCF is useful in simplifying fractions, finding common denominators, and in several applications of number theory. In this case, since 20 is a factor of both 80 and 20, it illustrates the concept of divisibility.
Tips
- Skipping Factor Listing: Some people may try to calculate the GCF directly without listing the factors, which can lead to errors. Always list the factors to avoid mistakes.
- Not Comparing All Common Factors: Ensure that all common factors are compared to find the largest one, as overlooking any can result in an incorrect GCF.
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