5) If the HCF of 55 and 99 is expressible in the form 55x + 99y, find x and y 6) find HCF of 65 and 117 and express it in the form 65x + 117y.Also find x and y
Answers
Given : 55 & 99 , 65 & 117
To find : HCF & express HCF in form 55x + 99y & 65x + 117y
Solution:
HCF of 55 & 99
99 = 55 *1 + 44
55 = 44*1 + 11
44 = 11 * 4
11 Is the HCF
55 = 44*1 + 11
=> 11 = 55 - 44*1
=> 11 = 55 - ( 99 - 55*1) * 1
=> 11 = 55 *2 + 99*(-1)
11 = 55x + 99y
x = 2 , y = -1
117 = 65 * 1 + 52
65 = 52 * 1 + 13
52 = 13 * 4
=> 13 is HCF
13 = 65 - 52* 1
=> 13 = 65 - (117 - 65 * 1)
=> 13 = 65 *2 + 117(-1)
13 = 65x + 117y
=> x = 2 , y = -1
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