Question

Find the hcf of 65 and 117 and express in form of 65 n and 1170

Answer 1

Between 65 and 117; 117 is greater than 65
 
Division lemma of 117 and 65:
 
⇒ 117 = 65 x 1 + 52
 
⇒ 65 = 52 x 1 + 13
 
⇒ 52 = 4 x 13 + 0
 
In this step the remainder is zero.
 
Thus, the divisor i.e. 13 in this step is the H.C.F. of the given numbers
 
The H.C.F. of 65 and 117 is 13
 
Now, 13 = 65 – 52 x 1
 
⇒ 52 = 117 – 65 x 1
 
⇒ 13 = 65 – (117 – 65 x 1) x 1
 
⇒ 13 = 65 x 2 – 117
 
⇒ 13 = 65 x 2 + 117 x (–1)
 
Therefore H.C.F. of 65 and 117 is of the form 65m + 117n, where m = 2 and n = –1.