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What Is the Greatest Common Factor for 48 and 60?

What Is the Greatest Common Factor for 48 and 60?

When working with numbers, finding the Greatest Common Factor (GCF) is a helpful skill that can simplify fractions, solve math problems, and even make everyday tasks like dividing things evenly much easier. So, what is the GCF for 48 and 60? Let’s break it down step by step.

Step 1: Understand the GCF

The GCF is the largest number that divides evenly into two or more numbers. In this case, we want the biggest number that divides both 48 and 60 without leaving a remainder.

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Step 2: List the Factors

First, list the factors of each number:

  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  • Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Step 3: Find the Common Factors

Now, look for numbers that appear in both lists:

  • Common Factors: 1, 2, 3, 4, 6, 12
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Step 4: Identify the Greatest Common Factor

From the common factors, the largest number is 12. Therefore, the GCF of 48 and 60 is 12.

Why Is the GCF Important?

The GCF is useful in many practical and mathematical applications, such as simplifying fractions. For example, if you’re simplifying the fraction 48/60, dividing the numerator and denominator by their GCF (12) gives you the simplest form: 4/5.

Finding the GCF doesn’t have to be complicated; once you get the hang of it, it’s a powerful tool to have in your math toolkit. Now that you know the GCF of 48 and 60 is 12, you can apply this process to any pair of numbers. Happy factoring!

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