The product of two numbers is 180. The LCM of the
two numbers is 60. What is the GCF of the numbers?
Explain how you know.
Jessica, Chandice, and Thomas or whoever -- please post your attempts to answer these 8 questions.
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To find the Greatest Common Factor (GCF) of two numbers, we need to prime factorize both numbers and then identify the common prime factors.
Given that the product of the two numbers is 180 and the least common multiple (LCM) is 60, we can start by finding the prime factorization of both 180 and 60.
Prime factorization of 180:
180 = 2 × 2 × 3 × 3 × 5
Prime factorization of 60:
60 = 2 × 2 × 3 × 5
Now we can identify the common prime factors from the prime factorization of both numbers:
Common prime factors: 2, 3, 5
To find the GCF, we multiply the common prime factors:
GCF = 2 × 3 × 5 = 30
Therefore, the GCF of the two numbers is 30.
In summary, we found the GCF by prime factorizing both numbers and determining the common prime factors. Then, multiplying the common prime factors gives us the GCF.