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GCF Problem Solving

Learn how to identify when to use the Greatest Common Factor or Least Common Multiple in word problems. Discover the concept of GCF, factors, common factors, and how GCF simplifies fractions. Test your knowledge with fun quiz questions!

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GCF Problem Solving

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  1. GCF Problem Solving How can you tell if a word problem requires you to use Greatest Common Factor or Least Common Multiple to solve?

  2. GCF Problem Solving • The highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions! • Greatest Common Factor is made up of three words • Greatest, • Common • Factor • Let us start with the last word:

  3. What is a "Factor" ? • Factors are the numbers you multiply together to get another number: • Sometimes we want to find ALL the factors of a number: • The factors of 12 are 1,2,3,4,6 and 12 ...... because 2 × 6 = 12, or 4 × 3 = 12, or 1 × 12 = 12.

  4. What is a "Common Factor" ? • Let us say you have worked out the factors of two or more numbers: • Example: • The factors of 12 are 1, 2, 3, 4, 6 and 12 • The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 • Then the common factors are those that are found in both numbers: • Notice that 1,2,3 and 6 appear in both lists? • So, the common factors of 12 and 30 are: 1, 2, 3 and 6 • It is a common factor when it is a factor of two or more numbers.(It is then "common to" those numbers.)

  5. What is the "Greatest Common Factor" ? • It is simply the largest of the common factors. In our previous example, the largest of the common factors is 15, so the Greatest Common Factor of 15, 30 and 105 is 15 • The "Greatest Common Factor" is the largest of the common factors (of two or more numbers)

  6. Why is this Useful? • One of the most useful things is when we want to simplify a fraction: • Example: How could we simplify 12/30? • At the top we found that the Common Factors of 12 and 30 were 1, 2, 3 and 6, and so the Greatest Common Factor is 6.

  7. Finding the Greatest Common Factor • Here are three ways: • 1. You can: • find all factors of both numbers • then select the ones that are common to both • then choose the greatest. • 2. You can find the prime factors and combine the common ones together • 3. And sometimes you can just play around with the factors until you discover it:

  8. QUIZ!!!!!! • On a sheet of notebook paper, tell the GCF/Solution of these problems

  9. Question #1 Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal # of crayons and equal # of paper.

  10. Question #2 • Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the larges tile she can use?

  11. Question #3 • I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?

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