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If (180=2^2\times3^2\times5), how many factors of (180) are perfect squares?
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Answer and explanation
Correct answer: (4)
Step 1: A square factor must have even exponents for every prime. Step 2: For (2), choices are (0,2); for (3), choices are (0,2); for (5), only (0). Total (=2\times2\times1=4). Step 3: Count only even exponent choices for square factors.
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What is the correct answer to this question?
(4)
Why is this the correct answer?
Step 1: A square factor must have even exponents for every prime. Step 2: For (2), choices are (0,2); for (3), choices are (0,2); for (5), only (0). Total (=2\times2\times1=4). Step 3: Count only even exponent choices for square factors.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Prime Factorisation.
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