The HCF of two numbers is (42) and their LCM is (2772). How many unordered pairs of such numbers are possible?
Answer and explanation
Correct answer: (4)
Step 1: Let the numbers be (42m) and (42n), where (m) and (n) are coprime. Step 2: (42mn=2772), so (mn=66=2\times3\times11). Splitting three distinct prime factors into two groups gives (4) unordered pairs. Step 3: While counting pairs, make sure (m) and (n) remain coprime.
Frequently asked questions
What is the correct answer to this question?
(4)
Why is this the correct answer?
Step 1: Let the numbers be (42m) and (42n), where (m) and (n) are coprime. Step 2: (42mn=2772), so (mn=66=2\times3\times11). Splitting three distinct prime factors into two groups gives (4) unordered pairs. Step 3: While counting pairs, make sure (m) and (n) remain coprime.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: HCF and LCM using prime factorisation.
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