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Factors, Prime Factorization, and Greatest Common Factor

Factors, Prime Factorization, and Greatest Common Factor. #12. Vocabulary. Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. 2. 6. 3. 6. 2. 3. =. ÷. =. 6 is divisible by 3 and 2. 3. 6. ÷. 2. =. Factors.

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Factors, Prime Factorization, and Greatest Common Factor

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  1. Factors, Prime Factorization, and Greatest Common Factor #12

  2. Vocabulary Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. 2 6 3 6 2 3 = ÷ = 6 is divisible by 3 and 2. 3 6 ÷ 2 = Factors Product

  3. Example 1: Finding Factors List all of the factors of the number 16. A. 16

  4. Example 2 List all of the factors of the number 12. A. 12

  5. Factorization of 12 Vocabulary You can use factors to write a number in different ways. Notice that these factors are all prime. 1 • 12 2 • 6 3 • 4 3 • 2 • 2 The prime factorization of a number is the number written as the product of its prime factors.

  6. Helpful Hint You can use exponents to write prime factorizations. Remember that an exponent tells you how many times the base is a factor.

  7. Example 3: Writing Prime Factorizations Write the prime factorization of 24. Method 1: Use a factor tree.

  8. Example 4: Writing Prime Factorizations Write the prime factorization of 45. Method 2: Use a ladder diagram. The prime factorization of45 is 3 • 3 • 5 or 32• 5 .

  9. Example 5 Write the prime factorization of 28. Method 1: Use a factor tree.

  10. Example 6 Write the prime factorization of 36. Method 2: Use a ladder diagram.

  11. Vocabulary Factors shared by two or more whole numbers are called common factors. The largest of the common factors is called the greatest common factor, or GCF. Factors of 24: Factors of 36: Common factors: 1, 2, 3, 4, 6, 8, 12, 24 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 6, 12 The greatest common factor (GCF) of 24 and 36 is 12. Example 1 shows three different methods for finding the GCF.

  12. Example 7: Finding the GCF Find the GCF of the set of numbers. 28 and 42 Method 1: List the factors.

  13. Example 8: Finding the GCF Find the GCF of the set of numbers. 18, 30, and 24 Method 2: Use the prime factorization.

  14. Example 9: Real-World Application Jenna has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is the greatest number of bouquets she can make?

  15. Example 10: Real-World Application Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each fruit in each basket. What is the greatest number of fruit baskets he can make?

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