Highest number which divides \(a, b, c\) leaving remainders \(x, y\) and \(z\) respectively, is HCF of  

\((a - x), (b - y), (c - z)\).

Highest number which when divides \(a, b, c\) leaves the same remainders is:

HCF of \((a - b), (b - c), (c - a)\)

Note that  \((a - b), (b - c), (c - a)\) are the positive difference of two numbers.

Lets try some questions on HCF.