If the HCF of 152 and 272 is expressible in the form 272x8+152x find x

1.	If the HCF of 152 and 272 is expressible in the form 272x8+152x find x
Answer» On applying the Euclid’s division lemma to find HCF of 152, 272, we get{tex}272 = 152\\times1 + 120{/tex}Here the remainder =\xa00.Using Euclid’s division lemma to find the HCF of 152 and 120, we get{tex}152 = 120\\times1 + 32{/tex}Again the remainder =\xa00.Using division lemma to find the HCF of 120 and 32, we get{tex}120 = 32\\times3 + 24{/tex}Similarly,{tex}32 = 24\\times1 + 8{/tex}{tex}24 = 8\\times3 + 0{/tex}HCF of 272 and 152 is 8.272{tex}\\times{/tex}8 + 152x = H.C.F. of the numbers{tex}\\Rightarrow {/tex}{tex}8 = 272\\times8 + 152x{/tex}\xa0{tex}\\Rightarrow{/tex}{tex}8 - 272\\times8 = 152x{/tex}{tex}\\Rightarrow 8(1- 272) = 152x{/tex}{tex}\\Rightarrow x = \\frac { - 2168 } { 152 } = \\frac { - 271 } { 19 }{/tex}\xa0

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