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If (N=2^a\times3^b) and (N) has (18) total factors, which pair is possible?
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Answer and explanation
Correct answer: (a=2,\ b=5)
Step 1: Total factors are ((a+1)(b+1)). Step 2: For (a=2,\ b=5), we get ((3)(6)=18). The other options do not give (18). Step 3: In option-based questions, substitute values into the rule quickly.
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What is the correct answer to this question?
(a=2,\ b=5)
Why is this the correct answer?
Step 1: Total factors are ((a+1)(b+1)). Step 2: For (a=2,\ b=5), we get ((3)(6)=18). The other options do not give (18). Step 3: In option-based questions, substitute values into the rule quickly.
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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