Find the greatest number that will divide 172, 205 and 304 so as to leave the same remainder in each case?

• A. 33
• B. None of these
• C. 99
• D. 66

Answer: (A)

The greatest number that will divide 172,205 and 304 leaving the same remainder in each    case is        HCF ((205-172), (304-205), (304-172))                = HCF of 33, 99, and 132        33=31x11                     99=3 x 3 x 11            132=3 x 2 x 2 x11     Required number =3 x 11=33