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Mastering Prime Factorization and Finding the Greatest Common Factor (GCF)

This lesson focuses on understanding prime factorization and how to find the greatest common factor (GCF) of numbers. Students will practice finding the prime factorization of several numbers such as 56, 75, 110, and 90. Through methods like listing factors and using prime factorization, learners will discover how to identify the GCF of different sets of numbers. By the end, students will also solve exercises to reinforce their understanding of divisibility by common numbers.

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Mastering Prime Factorization and Finding the Greatest Common Factor (GCF)

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  1. Warm-up Find the prime factorization for the following: 56 2) 75 3) 110 4) 90 5) What is a number divisible by 2,3,4,5,6,8,9,and 10? (Answers may vary)

  2. Warm-up Answer 1) 23 * 7 2) 3 * 52 3) 2 * 5 * 11 4) 2 * 32 * 5

  3. Vocabulary • Greatest common factor (GCF) – the largest common factor of two or more given numbers

  4. Greatest Common Factor (GCF) • What is a factor? • There are two methods to find the GCF • LIST METHOD • PRIME FACTORIZATION METHOD

  5. Greatest Common Factor (GCF) 1 - LIST METHOD • List all the factors of each number • Circle the greatest factor that is all the lists

  6. Greatest Common Factor (GCF) 2 – PRIME FACTORIZATION METHOD • Write the prime factorization of each number and circle the common prime factors • Multiply the common prime factors

  7. Something else to think about . . . With the prime factorization method, you can figure out the GCF using exponential form. 2² x 3 x 5 2³ x 3² x 5 x 7 Use the powers they have in common. So they share 2² and 3 and 5. Now multiply these together and get 60—the GCF.

  8. Greatest Common Factor (GCF) EXAMPLE 1: Find the GCF using a list. a. 28 and 42

  9. Greatest Common Factor (GCF) EXAMPLE 1: Find the GCF using a list. b. 12, 36, and 54

  10. Greatest Common Factor (GCF) EXAMPLE 2: Find the GCF using prime factorization. a. 30, 56

  11. Greatest Common Factor (GCF) EXAMPLE 2: Find the GCF using prime factorization. a. 45, 18, 27

  12. Greatest Common Factor (GCF) • EXAMPLE 3: 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 great number of bouquets she can make?

  13. Greatest Common Factor (GCF) • Now you try…find the GCF of the set of numbers: • 12 and 15 2) 36 and 45

  14. HOMEWORK GCF Crossword Puzzle

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