QQuestionMathematics
QuestionMathematics
What is the GREATEST perfect square that is a factor of 180?
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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 180
180 = 2^{2} \times 3^{2} \times 5
Step 3:: Identify the perfect square factors
- $$5^{0}$$ is also a perfect square (1)
To create a perfect square, we need to use even powers of prime factors. From the prime factorization, we can see:
Step 4:: Determine the largest perfect square factor
\sqrt{2^{2} \times 3^{2}} = 2^{1} \times 3^{1} = 6^{2} = 36
The largest perfect square will use the maximum even powers of each prime factor:
Step 5:: Verify the result
- 36 is a factor of 180 ($$180 \div 36 = 5$$)
- 36 is a perfect square - No larger perfect square divides 180 evenly
Final Answer
36
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