What is the greatest common factor of 72 and 64?
Understand the Problem
The question is asking for the greatest common factor (GCF) of the numbers 72 and 64. To solve this, we need to identify the factors of both numbers and then determine the largest factor they share.
Answer
The greatest common factor (GCF) of 72 and 64 is $8$.
Answer for screen readers
The greatest common factor (GCF) of 72 and 64 is $8$.
Steps to Solve
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List the factors of 72
To find the factors of 72, we can divide it by all integers from 1 to 72. The factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 -
List the factors of 64
Similarly, we will list all the factors of 64:
1, 2, 4, 8, 16, 32, 64 -
Identify common factors
Now, we need to find the common factors between the two lists:
Common factors: 1, 2, 4, 8 -
Determine the greatest common factor (GCF)
From the common factors, the largest one is the GCF. In this case, the greatest common factor is:
$$ \text{GCF} = 8 $$
The greatest common factor (GCF) of 72 and 64 is $8$.
More Information
The GCF is the largest number that can exactly divide both numbers without leaving a remainder. Knowing the GCF is helpful for simplifying fractions and solving problems involving ratios.
Tips
- Forgetting to list all factors: Make sure to check all integers up to the number being analyzed to ensure no factors are missed.
- Not identifying the largest common factor: Sometimes, students might miss selecting the largest factor when they find the common ones. Always check which common factor is the highest.
