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If (N=2^3\times3^4\times5), how many factors of (N) are divisible by (9) but not by (5)?
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Answer and explanation
Correct answer: (12)
Step 1: Since (9=3^2), power of (3) must be at least (2). Not divisible by (5) means power of (5) must be (0). Step 2: Choices are (4) for (2), (3) for (3), and (1) for (5). Total (=12). Step 3: Convert each condition into exponent restrictions.
Frequently asked questions
What is the correct answer to this question?
(12)
Why is this the correct answer?
Step 1: Since (9=3^2), power of (3) must be at least (2). Not divisible by (5) means power of (5) must be (0). Step 2: Choices are (4) for (2), (3) for (3), and (1) for (5). Total (=12). Step 3: Convert each condition into exponent restrictions.
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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