If (x=2^a\times3^4\times5) and (y=2^3\times3^b\times7) have HCF (2^2\times3^2), which statement about (a) and (b) is correct?
Answer and explanation
Correct answer: (a=2) and (b=2) are possible
Step 1: In HCF, the smaller power of each common prime is used. Step 2: For prime (2), the smaller power must be (2), so (a=2) is possible; for prime (3), (b=2) is possible. Step 3: In unknown power questions, focus on the minimum-power condition.
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What is the correct answer to this question?
(a=2) and (b=2) are possible
Why is this the correct answer?
Step 1: In HCF, the smaller power of each common prime is used. Step 2: For prime (2), the smaller power must be (2), so (a=2) is possible; for prime (3), (b=2) is possible. Step 3: In unknown power questions, focus on the minimum-power condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: HCF and LCM using prime factorisation.
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