For any integers a and b with HCF (a, b) = 1, what is HCF

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For any integers a and b with HCF (a, b) = 1, what is HCF (a + b, a - b) equal to?

1. It is always 1
2. It is always 2
3. Either 1 or 2
4. None of the above

Correct Option: C

Putting arbitrary values of a and b.

IIIustration 1:
Let a = 9 and b = 8
HCF (8 + 9, 9 - 8)
HCF (17, 1) = 1

IIIustration 2:
Let a = 23 and b =17
HCF (17 + 23, 23 -17)
HCF ( 40, 6) = 2

Hence, HCF (a + b, a - b) can either be 1 or 2.