How many factors of (2^5 \times 5^4) will be divisible by (10)?
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Answer and explanation
Correct answer: 20
Step 1: A factor divisible by (10) must contain at least one (2) and one (5). Step 2: Exponent choices for (2) are (1) to (5), so (5) choices; for (5), (1) to (4), so (4) choices. Total (20). Step 3: Divisibility by (10) needs both prime factors.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Step 1: A factor divisible by (10) must contain at least one (2) and one (5). Step 2: Exponent choices for (2) are (1) to (5), so (5) choices; for (5), (1) to (4), so (4) choices. Total (20). 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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