QQuestionMathematics
QuestionMathematics
What is the greatest perfect square that is a factor of 90?
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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 90
90 = 2 \times 3^{2} \times 5
Step 3:: Identify the possible perfect square factors
- $$5^{0}
To create a perfect square, we need to use even powers of prime factors. From the prime factorization, we can use:
Step 4:: Construct the largest perfect square factor
2^{0} \times 3^{2} \times 5^{0} = 1 \times 9 \times 1 = 9
The largest perfect square will use the maximum even powers:
Step 5:: Verify the result
- 9 is a perfect square ($$3^{2}$$)
- 9 is a factor of 90 (90 \div 9 = 10) - No larger perfect square exists as a factor of 90
Final Answer
9
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