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QuestionMathematics
What is the greatest perfect square that is a factor of 192?
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Answer
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Step 1:I'll solve this step by step using the specified LaTeX formatting guidelines:
Step 2:: Find the prime factorization of 192
192 = 2^{6} \times 3^{0}
- First, break down 192 into its prime factors
Step 3:: Identify the perfect square factors
- A perfect square is formed by taking prime factors with even exponents - From the prime factorization, we want to use the largest even power of 2
Step 4:: Determine the largest perfect square factor
- The largest even power of 2 in 192 is $$2^{6}
- 2^{6} = 64
Step 5:: Verify the result
64 = 8^{2}
- Check that 64 is indeed a factor of 192 - Confirm that 64 is a perfect square
Final Answer
64 is the greatest perfect square that is a factor of 192.
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