Presentation on theme: "Using Prime Factorizations: How can prime factorizations help us find the GCF and LCM of two numbers????"— Presentation transcript:
Using Prime Factorizations: How can prime factorizations help us find the GCF and LCM of two numbers????
Prime Factorization Defn: The prime factorization of a number is a string of factors made up of only prime numbers.
The GCF: Find the Prime Factorization of 24 and 60. 24 = and 60 = Work with your partner: What would be the GCF of 24 and 60?
The GCF would be the product of the longest string of prime factors that the numbers have in common. For example, the longest string of factors 24 and 60 have in common is 2 x 2 x 3. So, the GCF of 24 and 60 is : 2 x 2 x 3 = 12
Now you try…. Using the idea of prime factorization, find the GCF for: 48 and 72 30 and 54
The LCM: 24 = 2 x 2 x 2 x 3 and 60 = 2 x 2 x 3 x 5 Work with your partner to come up with a way to find the LCM of 24 and 60 using their prime factorizations.
The least common multiple of two numbers is the product of the shortest string that contains the prime factorizations of BOTH numbers. For example: the shortest string that contains the prime factorizations of 24 and 60 is: 2 x 2 x 2 x 3 x 5
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