Question

The greatest number that will divide $137,182$ and $422$ leaving a remainder of $2$ in each case is

Answer 1

In order to make 137, 182 and 422 completely divisible by the greatest number, we need to subtract 2 from each term, so

137-2 = 135, 182-2 = 180 and 422-2 = 420

Now HCF of 135, 180 and 420 is

135 = 3×3×3×5

180 = 2×2×3×3×5

420 = 2×2×3×5×7

Hence HCF of 135, 180 and 420 is 3×5 = 15

Hence the greatest number that will divide 137, 182 and 422 leaving the remainder 2 in each case is 15.

So the correct answer is 15.