What is the greatest common factor of 8 and 36?

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To determine the greatest common factor (GCF) of 8 and 36, we can use a few different methods, but one of the simplest is to list out the factors of each number and see what they have in common.

Step 1: List the factors

First, let’s find the factors of each number:

  • Factors of 8: 1, 2, 4, 8
  • Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Step 2: Identify the common factors

Next, we identify the common factors of 8 and 36. Looking at the lists above, we can see that the common factors are:

  • 1
  • 2
  • 4

Step 3: Find the greatest common factor

Now, we simply need to pick the greatest of those common factors. Among 1, 2, and 4, the largest number is:

  • 4

Therefore, the greatest common factor (GCF) of 8 and 36 is 4.

Conclusion: The GCF is an essential concept in mathematics, particularly useful in simplifying fractions and finding common denominators. Understanding how to determine the GCF can help with these tasks and improve overall mathematical proficiency.

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