For any integers 'a' and 'b' with HCF (a,b)= 1, what is HCF (a + b, a-b) equal to?
Correct Answer: Description for Correct answer:
For any integer 'a' and 'b', H.C.F. (a, b)= 1
for a = 5, b = 3 = > H.C.F.(5, 3) = 1
and H.C.F(5 + 3, 5-3) = H.C.F(8, 2) = 2
Now for a = 3, b = 2, H.C.F(a,b)= 1
and H.C.F(3 + 2, 3 - 2) = H.C.F(B, 1) = 1
Hence it can be concluded that for any integer 'a' and 'b' with H.C.F(a,b)= 1, the H.C.F. (a + b, a - b)will always be equal to either 1 or 2.
Hence option (C)is correct.
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