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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.