Let a,b be positive integers. What is HCF \( \Large \frac{a}{HCF(a,b)} \) \( \Large \frac{b}{HCF(a,b)} \) equal to?
Correct Answer: Description for Correct answer:
Let us consider any value of a, b such that a and b are positive integer.
For a=21 and b = 12
H.C.F (a, b)= H.C.F(21, 12) = 3.
Now H.C.F \( \Large \left(\frac{a}{H.C.F.(a,b)},\frac{b}{H.C.F.(a,b)} \right) \)
\( \Large = H.C.F. \left(\frac{21}{3},\frac{12}{3}\right) \)
= H.C.F. (7, 4) = 1
For any value of positive integer a and b H.C.F.
\( \Large \left(\frac{a}{H.C.F.(a,b)},\frac{b}{H.C.F.(a,b)} \right) \) will always give '1' as answer.
Hence option (c) is correct.
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