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

**Ans:**

By prime factorisation, we solve 85 and 238 one by one:

85 = 5 x 17

238 = 2 x 7 x 17

**Hence the HCF of these two numbers = 17**

Since it is given that the HCF is expressed by: 85 m – 238

∴ 85 m – 238 = 17

∴ 85 m = 17 + 238

∴ 85 m = 255

∴ m =

∴ m =

∴ m = 3

**Therefore, value of m is 3**

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