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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