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How many factors of (2^5 \times 3^2) will be divisible by (3)?
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Answer and explanation
Correct answer: 12
Step 1: A factor divisible by (3) must have exponent of (3) at least (1). Step 2: The exponent of (2) has (6) choices from (0) to (5), and the exponent of (3) has (2) choices (1,2). Total (6 \times 2=12). Step 3: In condition-based questions, adjust exponent limits carefully.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Step 1: A factor divisible by (3) must have exponent of (3) at least (1). Step 2: The exponent of (2) has (6) choices from (0) to (5), and the exponent of (3) has (2) choices (1,2). Total (6 \times 2=12). Step 3: In condition-based questions, adjust exponent limits carefully.
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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