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How many factors of (2^4 \times 3^3) will be divisible by (3)?
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Answer and explanation
Correct answer: 15
Step 1: A factor divisible by (3) must have the exponent of (3) at least (1). Step 2: The exponent of (2) has (5) choices from (0) to (4), and the exponent of (3) has (3) choices (1,2,3). Total (5 \times 3=15). Step 3: In conditional factor counting, adjust exponent limits.
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What is the correct answer to this question?
15
Why is this the correct answer?
Step 1: A factor divisible by (3) must have the exponent of (3) at least (1). Step 2: The exponent of (2) has (5) choices from (0) to (4), and the exponent of (3) has (3) choices (1,2,3). Total (5 \times 3=15). Step 3: In conditional factor counting, adjust 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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