If (m=2^3\times3^2\times5^2), how many factors of (m) are divisible by (10)?
Answer and explanation
Correct answer: (18)
Step 1: Since (10=2\times5), the factor must contain at least one (2) and one (5). Step 2: Powers of (2): (1,2,3) give (3) choices; powers of (3): (0,1,2) give (3) choices; powers of (5): (1,2) give (2) choices. Total (=18). Step 3: For divisibility, check the required minimum prime powers.
Frequently asked questions
What is the correct answer to this question?
(18)
Why is this the correct answer?
Step 1: Since (10=2\times5), the factor must contain at least one (2) and one (5). Step 2: Powers of (2): (1,2,3) give (3) choices; powers of (3): (0,1,2) give (3) choices; powers of (5): (1,2) give (2) choices. Total (=18). Step 3: For divisibility, check the required minimum prime powers.
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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