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If (x=2^a\times3^5\times5) and (y=2^6\times3^b\times7) have HCF (2^4\times3^3), which values are possible?
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Answer and explanation
Correct answer: (a=4), (b=3)
Step 1: HCF uses the smaller power of each common prime. Step 2: The smaller power of (2) must be (4), so (a=4) is possible; the smaller power of (3) must be (3), so (b=3) is possible. Step 3: Check unknown powers separately for each prime base.
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What is the correct answer to this question?
(a=4), (b=3)
Why is this the correct answer?
Step 1: HCF uses the smaller power of each common prime. Step 2: The smaller power of (2) must be (4), so (a=4) is possible; the smaller power of (3) must be (3), so (b=3) is possible. Step 3: Check unknown powers separately for each prime base.
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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