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Example 4-1a

Example 4-1a. Find the GCF of 16 and 24 . Method 1 List the factors. factors of 16: 1 , 2 , 4 , 8 , 16. factors of 24: 1 , 2 , 3, 4 , 6, 8 , 12, 24. Answer: The greatest common factor of 16 and 24 is 8 . Example 4-1a. Find the GCF of 16 and 24 .

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Example 4-1a

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  1. Example 4-1a Find the GCF of 16 and 24. Method 1List the factors. factors of 16: 1, 2, 4, 8, 16 factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Answer: The greatest common factor of 16 and 24 is 8.

  2. Example 4-1a Find the GCF of 16 and 24. Method 2Use prime factorization. The GCF is the product of the common prime factors. Again, the GCF of 16 and 24 is 8. Answer: 8

  3. Example 4-1c Find the GCF of 18 and 30. Answer: 6

  4. Example 4-2a Find the GCF of 28 and 35. First, factor each number completely. The common prime factor is 7. Answer: The GCF of 28 and 35 is 7.

  5. Answer: The GCF of 12, 48, and 72 is . Example 4-2b Find the GCF of 12, 48, and 72. First, factor each number completely. The common prime factors are 2, 2, and 3.

  6. a. 24, 32 b. 30, 42, 60 Example 4-2c Find the GCF of each set of numbers. Answer: 8 Answer: 6

  7. Example 4-3a Cookie SaleParents donated 150 chocolate chip cookies and 120 molasses cookies for a school bake sale. If the cookies are arranged on plates, and each plate has the same number of chocolate chip cookies and the same number of molasses cookies, what is the largest number of plates possible? Find the GCF of 150 and 120. The common prime factors are 2, 3, and 5.

  8. The GCF of 150 and 120 is or 30. Example 4-3a Answer: So, 30 plates are possible.

  9. Example 4-3b Cookie SaleParents donated 150 chocolate chip cookies and 120 molasses cookies for a school bake sale. How many chocolate chip and molasses cookies will be on each plate? Answer: So, each plate will have 5 chocolate chip cookies and 4 molasses cookies.

  10. a. If the apples are arranged in baskets, and each basket has the same number of red apples and the same number of green apples, what is the largest number of baskets possible? b. How many red apples and green apples will be in each basket? Example 4-3c ApplesThere are 96 red apples and 72 green apples to be placed in baskets. Answer: 24 baskets Answer: 4 red apples and 3 green apples

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  13. Number Prime Factorization Exponential Form 168 180 Example 6-1a Find the LCM of 168 and 180. The prime factors of both numbers are 2, 3, 5, and 7. Multiply the greatest powers of 2, 3, 5, and 7 appearing in either factorization. Answer: The LCM of 168 and 180 is 2520.

  14. Example 6-1b Find the LCM of 144 and 96. Answer: 288

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