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How do you use prime factorization to find the GCF or LCM of two whole numbers?

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## How do you use prime factorization to find the GCF or LCM of two whole numbers?

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**How do you use prime factorization to find the GCF or LCM of**two whole numbers? For example, how do you use prime factors to find the GCF and LCM of 8 and 30?**In this lesson you will learn how to find the GCF and LCM of**two whole numbers by using their prime factors.**Prime numbers have only two factors, one and themselves.**7 is a prime number. 7 x 1 = 7 The first few prime numbers are 2, 3, 5, 7, 11, 13, 17… Composite numbers have more than two factors. 10 is a composite number. 1 x 10 = 10 2 x 5 = 10**The first few prime numbers are 2, 3, 5, 7, 11, 13, 17…**Prime factorization is finding a string of prime numbers that when multiplied result in your original number. factor tree 40 2 x 20 40 = 2 x 2 x 2 x 5 2 x 10 All composite numbers can be written as a string of prime factors. 2 x 5**Confusing factors with multiples**Find the factors of 25. 1, 5, 25 25, 50, 75…**Remembering to find only prime factors for a number when**using prime factorization. The prime factors of 20 are 2 x 10.**How do you use prime factorization to find the GCF and LCM**of 8 and 30? factor tree = 2 x 2 x 2 8 = 2 x 3 x 5 30 2 x 4 2 x 15 2 x 2 3 x 5**Venn Diagram**8 GCF = 2 x 2 x 2 30 = 2 x 3 x 5 The GCF of 8 and 30 is 2. The LCM of 8 and 30 is 120. 2 2 2 3 5 LCM 2 x 2 x 2 x 3 x 5 = 120**What is the GCF and LCM of 18 and 27?**= 3 x 3 x 3 27 = 2 x 3 x 3 18 2 x 9 3 x 9 3 x 3 3 x 3**18**= 2 x 3 x 3 Venn Diagram 3 x 3 = 9 GCF 27 = 3 x 3 x 3 The GCF of 18 and 27 is 9. The LCM of 8 and 30 is 54. 2 3 3 3 LCM 2 x 3 x 3 x 3 = 54**In this lesson you have learned how to find the GCF and LCM**of two whole numbers by using their prime factors.