Question

If the HCF of A, B and C is x, is the HCF of A -B, B-C and A-C also x? If not always, under what condition will it be equal to x?​

Answer 1

Given, HCF (A, B, C) = x.

Say, A = x * p, B = x * q and C = x * r; where p, q, r are coprime numbers and p, q, r ≠ 0.

(A - B) = x * (p - q)

(B - C) = x * (q - r)

(A - C) = x * (p - r)

If HCF {(A - B), (B - C), (A - C)} = x; then:-

(p - q), (q - r), (p - r) must be coprime numbers and (p - q), (q - r), (p - r) ≠ 0.

That is, (p - q), (q - r), (p - r) must be coprime numbers and p ≠ q ≠ r ≠ 0.