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,

153 = 85 x 2 + 68

85 = 68 x 1 + 17

68 = 17 x 4 + 0

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

From given data HCF is written as: 

85m - 238 = 17 

85m = 17 + 238 

85m = 255

\(m = \frac {255}{85}\)

\(\therefore\) m = 3

Answer 2

85 = 5 x 17

238 = 2 x 7 x 17 

HCF(85, 238) = 17 

17 = 85 x m - 238 

m = 3