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If (N=2^4\times3^2\times5^3), how many factors of (N) are divisible by (25)?
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Answer and explanation
Correct answer: (30)
Step 1: Since (25=5^2), the factor must contain at least (5^2). Step 2: Choices for (2): (5), for (3): (3), for (5): (2) or (3), giving (2) choices. Total (=5\times3\times2=30). Step 3: Treat (25) as (5^2) before counting.
Frequently asked questions
What is the correct answer to this question?
(30)
Why is this the correct answer?
Step 1: Since (25=5^2), the factor must contain at least (5^2). Step 2: Choices for (2): (5), for (3): (3), for (5): (2) or (3), giving (2) choices. Total (=5\times3\times2=30). Step 3: Treat (25) as (5^2) before counting.
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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