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Transparency 1. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 1-4b. Objective. Find the greatest common factor of two or more numbers. Example 1-4b. Vocabulary. Venn diagram.

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  1. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 1-4b Objective Find the greatest common factor of two or more numbers

  4. Example 1-4b Vocabulary Venn diagram The use of circles to show how elements among sets of numbers or objects are related

  5. Example 1-4b Vocabulary Greatest common factor (GCF) The greatest of the common factors of two or more numbers

  6. Example 1-4b Review Vocabulary Factor Two or more numbers that are multiplied together to form a product

  7. Example 1-4b Review Vocabulary Prime number A whole number that has exactly two factors, 1 and the number itself

  8. Lesson 1 Contents Example 1Find the GCF by Listing Factors Example 2Find the GCF by Using Prime Factors Example 3Use the GCF to Solve a Problem 1/3

  9. Example 1-1a Find the GCF of 36 and 48 To find the Greatest Common Factor (GCF) You must prime factor the numbers 48 36 Write the numbers Put an upside down division sign with the numbers 1/3

  10. Example 1-1a Find the GCF of 36 and 48 Prime factor 36 2 36 36 is an even number and the prime number 2 always goes into an even number 18 Place 2 outside the house Divide 36 by 2 Put 18 below 36 Ask “is 18 a prime number?” 1/3

  11. Example 1-1a Find the GCF of 36 and 48 Ask “is 18 a prime number?” 2 will go into 18 evenly 2 36 18 2 Put the prime factor bar on 18 9 Place 2 outside the bar Divide 18 by 2 Place 9 under 18 Ask “is 9 a prime number?” 1/3

  12. Example 1-1a Find the GCF of 36 and 48 Ask “is 9 a prime number?” 2 36 3 will go into 9 evenly and 3 is a prime number 18 2 9 3 Put the prime factor bar on 9 3 Place 3 outside the bar Divide 9 by 3 Place 3 under 9 1/3

  13. Example 1-1a Find the GCF of 36 and 48 Ask “is 3 a prime number?” 2 2 48 36 3 is a prime number so you are done prime factoring 36 18 2 9 3 Now prime factor 48 3 Ask “is 48 a prime number?” 2 will go into 48 because it is even Place 2 outside the bar 1/3

  14. Example 1-1a Find the GCF of 36 and 48 Divide 48 by 2 Place 24 under 48 2 2 48 36 18 2 2 24 Ask “is 24 a prime number?” 9 3 2 will go into 24 because it is even 3 Put the prime factor bar on 24 Place 2 outside the bar 1/3

  15. Example 1-1a Find the GCF of 36 and 48 Divide 24 by 2 Place 12 under 24 2 2 48 36 18 2 2 24 Ask “is 12 a prime number?” 12 2 9 3 2 will go into 12 because it is even 3 Put the prime factor bar on 12 Place 2 outside the bar 1/3

  16. Example 1-1a Find the GCF of 36 and 48 Divide 12 by 2 Place 6 under 12 2 2 48 36 18 2 2 24 Ask “is 6 a prime number?” 12 2 9 3 2 will go into 6 because it is even 6 2 3 Put the prime factor bar on 6 Place 2 outside the bar 1/3

  17. Example 1-1a Find the GCF of 36 and 48 Divide 6 by 2 Place 3 under 6 2 2 48 36 18 2 2 24 Ask “is 3 a prime number?” 12 2 9 3 3 is a prime number so you are done prime factoring 48 6 2 3 3 Circle factors that are common in each number and write as factors There are no more common factors 2  2  3 2  2  2 1/3

  18. Example 1-1a Find the GCF of 36 and 48 2 2 48 36 18 2 2 24 12 2 9 3 Multiply the common factors 6 2 3 Identify the product as GCF 3 2  2  3 Answer: 12 = GCF 12 1/3

  19. Example 1-1c Find the GCF of 45 and 75 Answer:15 = GCF 1/3

  20. Example 1-2a Find the GCF of 52 and 78 Prime factor both 52 and 78 78 2 2 52 39 26 3 2 13 13 Circle factors that are common in each number and write as factors Multiply the common factors 2  13 Identify the product as GCF Answer: = GCF 26 2/3

  21. Example 1-2c Find the GCF of 64 and 80 by using prime factors. Answer:16 = GCF 2/3

  22. Example 1-3a SALESAnnessa sold bags of cookies at a bake sale. She sold small, medium, and large bags, with a different number of cookies in each size bag. By the end of the sale, she used 18 cookies to fill the small bags, 27 cookies to fill the medium bags, and 45 cookies to fill the large bags. She sold the same number of bags for the three sizes. What is the greatest number of bags that she could have sold? Find the factors of 18, 27, and 45 3/3

  23. Example 1-3b 27 18 3 2 45 5 3 9 9 9 3 3 3 3 3 Circle factors that are common in each number and write as factors 3  3 Multiply the common factors 9 = GCF Identify the product as GCF Answer: The greatest number of bags she could have sold is 9 of each size 3/3

  24. Example 1-3c * CANDYSarah is making bags of candy for a school fund-raiser. She is making three different sizes of bags. By the time Sarah had finished making the bags, she had used 24 lollipops to fill the small bags, 40 lollipops to fill the medium bags, and 64 lollipops to fill the large bags. She completed the same number of bags for the three sizes. What is the greatest number of bags she could have made? Answer:24 bags 3/3

  25. End of Lesson 1 Assignment

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