Greatest Common Factors

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What is the Greatest Common Factor (GCF)?

The Greatest Common Factor of two or more numbers is the largest number that divides each of the numbers without leaving any remainder. In other words, it’s the biggest number that is a factor of all the given numbers.

Finding the GCF

To find the GCF of two or more numbers, first, list the factors of each number and then identify the largest factor that they have in common.

Real-life Examples

  1. Cutting Ribbon: Imagine you have two pieces of ribbon, one 18 inches long and another 24 inches long. You want to cut them into equal lengths with no ribbon left over and the pieces as long as possible. To find out the length of each piece, find the GCF of 18 and 24. The factors of 18 are 1, 2, 3, 6, 9, 18, and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The largest common factor is 6, so you can cut the ribbons into pieces 6 inches long.
  2. Arranging Chairs in Rows: Suppose you’re setting up chairs for an event and you have 30 chairs and 45 chairs in two different colors. You want to arrange them in equal rows with both colors in each row and the rows as large as possible. The GCF of 30 and 45 will give you the number of chairs in each row. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30, and the factors of 45 are 1, 3, 5, 9, 15, 45. The largest common factor is 15, so you can arrange the chairs in rows of 15.

Steps to Find the GCF

  1. List the Factors: Write down all the factors of each number.
  2. Find Common Factors: Identify the factors common to all the numbers.
  3. Choose the Largest One: The largest of these common factors is your GCF.

Example of Finding the GCF

Let’s find the GCF of 32 and 48:

  • Factors of 32: 1, 2, 4, 8, 16, 32
  • Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The common factors are 1, 2, 4, 8, 16 and the largest is 16. So, the GCF of 32 and 48 is 16.

Why is the GCF Important?

In real life, the GCF is useful for dividing things into smaller sections, ensuring even distribution, and maximizing the use of resources without waste.

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