Question

Find the greatest number which divides 34,60 And 85 leaving remainder 7,6 and 4 respectively

Answer 1

Since 7, 6 and 4 are the remainders of 34, 60 and 85 respectively.
So required number should divide (34 - 7) i.e. 27; (60 - 6) i.e. 54 and (85 - 4) i.e. 81 completely.
Thus required number = H.C.F of 27, 54 and 81.
Now we have;
27 = 3×3×354 = 3×3×3×281 = 3×3×3×3
So; H.C.F of 27, 54 and 81 = 3×3×3 = 2727 = 3×3×354 = 3×3×3×281 = 3×3×3×3
So; H.C.F of 27, 54 and 81 = 3×3×3 = 27
Therefore the required number is 27.