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If (n=2^5\times3^4\times7), how many factors of (n) are not divisible by (6)?
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Answer and explanation
Correct answer: (22)
Step 1: Total factors are ((5+1)(4+1)(1+1)=60). Step 2: Factors divisible by (6=2\times3) must have power of (2) at least (1) and power of (3) at least (1), so (5\times4\times2=40). Step 3: Not divisible by (6) means total minus divisible factors, (60-40=20).
Frequently asked questions
What is the correct answer to this question?
(22)
Why is this the correct answer?
Step 1: Total factors are ((5+1)(4+1)(1+1)=60). Step 2: Factors divisible by (6=2\times3) must have power of (2) at least (1) and power of (3) at least (1), so (5\times4\times2=40). Step 3: Not divisible by (6) means total minus divisible factors, (60-40=20).
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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