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Write the prime factorization of numbers. Find the GCF of monomials.

Objectives. Write the prime factorization of numbers. Find the GCF of monomials. Vocabulary. prime factorization greatest common factor. 1 12. 3 4. 1 4 3. . . . . 2 6. 2 2 3. . . .

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Write the prime factorization of numbers. Find the GCF of monomials.

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  1. Objectives Write the prime factorization of numbers. Find the GCF of monomials.

  2. Vocabulary prime factorization greatest common factor

  3. 1 12 3 4 1 4 3     2 6 2 2 3    The whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. You can use the factors of a number to write the number as a product. The number 12 can be factored several ways. Factorizations of 12

  4. Remember! A prime number has exactly two factors, itself and 1. The number 1 is not prime because it only has one factor.

  5. 98 2 98 49  7 2 49 7 7  7 7 1 98 = 2 7 7 98 = 2 7 7     Example 1: Writing Prime Factorizations Write the prime factorization of 98. Method 1 Factor tree Method 2 Ladder diagram Choose any two factors of 98 to begin. Keep finding factors until each branch ends in a prime factor. Choose a prime factor of 98 to begin. Keep dividing by prime factors until the quotient is 1. The prime factorization of 98 is 2  7  7 or 2 72.

  6. 40 33 11  2 20 3  2 10  2 5 Check It Out! Example 1 Write the prime factorization of each number. a. 40 b. 33 40 = 23 5 33 = 3  11 The prime factorization of 40 is 2  2  2  5 or 23 5. The prime factorization of 33 is 3  11.

  7. 19 1 49 19  7 7 Check It Out! Example 1 Write the prime factorization of each number. c. 49 d. 19 49 = 7  7 19 = 1  19 The prime factorization of 49 is 7  7 or 72. The prime factorization of 19 is 1  19.

  8. Factors that are shared by two or more whole numbers are called common factors. The greatest of these common factors is called the greatest common factor, or GCF. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 32: 1, 2, 4, 8, 16, 32 Common factors: 1, 2, 4 The greatest of the common factors is 4.

  9. Example 2A: Finding the GCF of Numbers Find the GCF of each pair of numbers. 100 and 60 Method 1 List the factors. factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 List all the factors. factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 Circle the GCF. The GCF of 100 and 60 is 20.

  10. Example 2B: Finding the GCF of Numbers Find the GCF of each pair of numbers. 26 and 52 Method 2 Prime factorization. Write the prime factorization of each number. 26 = 2  13 52 = 2  2  13 Align the common factors. 2  13 = 26 The GCF of 26 and 52 is 26.

  11. Check It Out! Example 2a Find the GCF of each pair of numbers. 12 and 16 Method 1 List the factors. List all the factors. factors of 12: 1, 2, 3, 4, 6, 12 Circle the GCF. factors of 16: 1, 2, 4, 8, 16 The GCF of 12 and 16 is 4.

  12. Check It Out! Example 2b Find the GCF of each pair of numbers. 15 and 25

  13. Example 3A: Finding the GCF of Monomials Find the GCF of each pair of monomials. 15x3 and 9x2

  14. Example 3B: Finding the GCF of Monomials Find the GCF of each pair of monomials. 8x2 and 7y3

  15. Check It Out! Example 3a Find the GCF of each pair of monomials. 18g2 and 27g3

  16. Check It Out! Example 3b Find the GCF of each pair of monomials. 16a6 and 9b

  17. Check It Out! Example 3c Find the GCF of each pair of monomials. 8x and 7v2

  18. Lesson Quiz: Part I Write the prime factorization of each number. 1. 50 2. 84 Find the GCF of each pair of numbers. 3. 18 and 75 4. 20 and 36 2  52 22 3  7 3 4

  19. Lesson Quiz: Part II Find the GCF of each pair of monomials. 5. 12x and 28x3 6. 27x2 and 45x3y2 7. Cindi is planting a rectangular flower bed with 40 orange flower and 28 yellow flowers. She wants to plant them so that each row will have the same number of plants but of only one color. How many rows will Cindi need if she puts the greatest possible number of plants in each row? 4x 9x2 17

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