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If the HCF of 152 and …

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

Posted by Yash Khalse 1 year ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 4 years, 8 months ago

On applying the Euclid’s division lemma to find HCF of 152, 272, we get

{tex}272 = 152\times1 + 120{/tex}
Here the remainder = 0.
Using Euclid’s division lemma to find the HCF of 152 and 120, we get
{tex}152 = 120\times1 + 32{/tex}
Again the remainder = 0.
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}

{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}

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