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How many factors of (2^4 \times 5^2) will be divisible by (10)?
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Answer and explanation
Correct answer: 8
Step 1: A factor divisible by (10) must contain both (2) and (5). Step 2: The exponent of (2) can be (1) to (4), giving (4) choices, and the exponent of (5) can be (1) to (2), giving (2) choices. Total (4 \times 2=8). Step 3: Divisibility by (10) needs both prime factors.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Step 1: A factor divisible by (10) must contain both (2) and (5). Step 2: The exponent of (2) can be (1) to (4), giving (4) choices, and the exponent of (5) can be (1) to (2), giving (2) choices. Total (4 \times 2=8). Step 3: Divisibility by (10) needs both prime factors.
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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