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If (N=2^4\times3^3\times5^2), how many factors of (N) are divisible by neither (2) nor (3)?
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Answer and explanation
Correct answer: (3)
Step 1: To be divisible by neither (2) nor (3), powers of (2) and (3) must both be (0). Step 2: Power of (5) can be (0,1,2), giving (3) factors. Step 3: For neither-nor conditions, set both restricted prime powers to zero.
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What is the correct answer to this question?
(3)
Why is this the correct answer?
Step 1: To be divisible by neither (2) nor (3), powers of (2) and (3) must both be (0). Step 2: Power of (5) can be (0,1,2), giving (3) factors. Step 3: For neither-nor conditions, set both restricted prime powers to zero.
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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