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Two numbers are (2^a\times 3^2\times 5) and (2^4\times 3^b\times 7). If their HCF is (2^3\times 3^2), which option is correct for ((a,b))?
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Answer and explanation
Correct answer: ((3,2))
Step 1: In the HCF, the exponent of (2) must be (\min(a,4)=3), so (a=3) fits. Step 2: The exponent of (3) must be (\min(2,b)=2), so (b\geq 2); among the options, ((3,2)) fits. Step 3: For unknown exponents, apply the smaller-exponent rule.
Frequently asked questions
What is the correct answer to this question?
((3,2))
Why is this the correct answer?
Step 1: In the HCF, the exponent of (2) must be (\min(a,4)=3), so (a=3) fits. Step 2: The exponent of (3) must be (\min(2,b)=2), so (b\geq 2); among the options, ((3,2)) fits. Step 3: For unknown exponents, apply the smaller-exponent rule.
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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