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If (N=2^5\times3^3\times5^2), how many factors of (N) are divisible by (12)?
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Answer and explanation
Correct answer: (48)
Step 1: (12=2^2\times3), so the factor needs power of (2) at least (2) and power of (3) at least (1). Step 2: Choices are (4) for (2), (3) for (3), and (3) for (5). Total (=4\times3\times3=36). Step 3: First write the divisor in prime form, then set exponent limits.
Frequently asked questions
What is the correct answer to this question?
(48)
Why is this the correct answer?
Step 1: (12=2^2\times3), so the factor needs power of (2) at least (2) and power of (3) at least (1). Step 2: Choices are (4) for (2), (3) for (3), and (3) for (5). Total (=4\times3\times3=36). Step 3: First write the divisor in prime form, then set exponent limits.
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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