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If the HCF 210 and 55 …

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If the HCF 210 and 55 is expressible in the form 210*5+55y.find y

Posted by Priyanshi Patel 6 years, 6 months ago

Sia ? 6 years, 6 months ago

First, find the HCF of 210 and 55 by Euclid's Division Algorithm

210 = 55 {tex}\times{/tex} 3 + 45

55 = 45 {tex}\times{/tex} 1 + 10

45 = 10 {tex}\times{/tex} 4 + 5

10 = 5 {tex}\times{/tex} 2 + 0 (zero remainder)

therefore, HCF (210 , 55) = 5

Now,

{tex}\therefore {/tex} {tex}5 = 210 \times 5 + 55y{/tex}

{tex} \Rightarrow {/tex} {tex}5 - 1050 = 55y{/tex}

{tex} \Rightarrow {/tex} {tex} - 1045 = 55y{/tex}

{tex} \Rightarrow {/tex} {tex}y = - 19{/tex}

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