Find the number which divides 411, 684, 821 and leaves remainder 3, 4 and 5 respectively.

136

HCF of (411 - 3), (684 - 4), (821 - 5)

          =   408        680         816

                 ↓             ↓             ↓

            3×136       5×136      6×136

∴ HCF = 136 is that number which divides 411, 684, 821 and leaves remainder 3, 4 and 5 respectively.