Find the greatest number that will divide 38, 88 and 163 so as to leave the same remainder in each case.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 25
If a number leaves the same remainder when it divides two numbers, it divides their difference with no remainder, because the remainders cancel. So the required number is the HCF of the differences.
Difference of the first two numbers: \(88-38=50\)
Difference of the last two: \(163-88=75\)
Difference of the first and last: \(163-38=125\)
The greatest number dividing all three differences is their HCF, 25