Question

The H.C.F of 85 and 238 is expressible in the form 85m -238. Find the value of m.

Answer 1

Using Euclid's division algorithm,

238 = 85 × 2 + 68

85 = 68 × 1 + 17

68 = 17 × 4 + 0

Since the remainder has come to zero, the HCF of the given numbers is 17.

From the given data, HCF is written as:

85m − 238 = 17

85m = 17 + 238

85m = 255

m = `255/85`

∴ m = 3