IF THE HCF OF 13 AND 65 IS EXPRESSIBLE IN THE FORM 65M-117N THEN HOW TO FIND THE VALUE OF M AND N
 

Asked by dalbirgolagarh | 16th Sep, 2015, 05:08: PM

Expert Answer:

The HCF and LCM of 13 and 65 can be found by writing both in prime factorised form. 
13 = 13
65 = 5 X 13
HCF = 13
So we have to write 13 as 65M - 117N.
We proceed using trial and error method by substituting different integer values of M and N.
M =1 will make 117N greater than 65M for all positive integer values of N. So, M=1 is not possible.
M=2 will imply 65M = 130. If we now use N =1, we get 117N=117. 130 - 117 = 13, which is the HCF.
Hence, we get M and N values by trial and error method as 2 and 1 respectively.
 

Answered by satyajit samal | 18th Sep, 2015, 12:30: AM

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