QQuestionMathematics
QuestionMathematics
What is the greatest perfect square that is a factor of 147?
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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 147
147 = 3 \times 7^{2}
• First, let's break down 147 into its prime factors
Step 3:: Identify the perfect square factors
- $$(3 \times 7)^{2} = 3^{2} \times 7^{2} = 9 \times 49 = 441$$ (but this is larger than 147)
• A perfect square is a number that can be expressed as the product of an integer with itself • The other possible perfect square factors are:
Step 4:: Determine the greatest perfect square factor
• The perfect square factors of 147 are 1 and 49 • 49 is the largest perfect square factor of 147
Final Answer
49
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