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If (N=2^6\times3^2\times7^2), how many factors (d) are there such that (d^2) also divides (N)?
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Answer and explanation
Correct answer: (32)
Step 1: If (d=2^a\times3^b\times7^c), then (d^2=2^{2a}\times3^{2b}\times7^{2c}). Step 2: Conditions are (2a\le6), (2b\le2), (2c\le2), so choices are (4,2,2). Total (=16). Step 3: For square divisibility, double the exponents and compare.
Frequently asked questions
What is the correct answer to this question?
(32)
Why is this the correct answer?
Step 1: If (d=2^a\times3^b\times7^c), then (d^2=2^{2a}\times3^{2b}\times7^{2c}). Step 2: Conditions are (2a\le6), (2b\le2), (2c\le2), so choices are (4,2,2). Total (=16). Step 3: For square divisibility, double the exponents and compare.
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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