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How many factors of (2^2 \times 3^3) will be divisible by (3)?
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Answer and explanation
Correct answer: 9
Step 1: A factor divisible by (3) must have exponent of (3) at least (1). Step 2: The exponent of (2) has (3) choices (0,1,2), and exponent of (3) has (3) choices (1,2,3). Total (3 \times 3=9). Step 3: For conditional factors, adjust exponent choices carefully.
Frequently asked questions
What is the correct answer to this question?
9
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 (3) choices (0,1,2), and exponent of (3) has (3) choices (1,2,3). Total (3 \times 3=9). Step 3: For conditional factors, adjust exponent choices 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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