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If (k=2^3\times3^2\times5^2\times7), how many factors of (k) are divisible by (15)?
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Answer and explanation
Correct answer: (32)
Step 1: Since (15=3\times5), the factor must contain both (3) and (5). Step 2: Power choices are (2:4) choices, (3:2) choices, (5:2) choices, and (7:2) choices. Total (=4\times2\times2\times2=32). Step 3: Start restricted prime powers from the minimum required value.
Frequently asked questions
What is the correct answer to this question?
(32)
Why is this the correct answer?
Step 1: Since (15=3\times5), the factor must contain both (3) and (5). Step 2: Power choices are (2:4) choices, (3:2) choices, (5:2) choices, and (7:2) choices. Total (=4\times2\times2\times2=32). Step 3: Start restricted prime powers from the minimum required value.
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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