Find the greatest number that will divide 38, 88 and 163 so as to leave the same remainder in each case.

25

We need to find the difference between the given numbers. If two numbers give the same reminder while divided by any other number, then their difference must give zero reminder when divided by the same number.

Therefore,

163 - 88 = 75

163 - 38 = 125

88 - 38 = 50

So the biggest number that divides all these numbers is = HCF of (125, 75 & 50) = 25

Hence,

The greatest number that will divide 38, 88 and 163 so as to leave the same remainder in each case is 25