Find the greatest number which divides 77, 147 and 252 leaves same remainder in each case.

77, 147, 252

Leaves same remainder means

$\Rightarrow (252-147)(147-77)(252-77)$

$\Rightarrow 105,70,175$

H.C.F.  $$\begin{gathered} \Rightarrow 105=3\times 5\times 7, \\ 70=2\times 5\times 7, \\ 175=5^2\times 7 \end{gathered}$$

$\text{H.C.F.}\Rightarrow 35$