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Express the HCF of 468 and …

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Express the HCF of 468 and 222 as 468+22y where x and y are integers in twice different ways

Posted by Bhumika Jaim 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given integers are 468 and 222, where 468 > 222
By applying Euclid’s division lemma, we get
468 = 222 {tex}\times{/tex} 2 + 24.
222 = 24 {tex}\times{/tex} 9 + 6.
24 = 6 {tex}\times{/tex} 4 + 0.
We observe that remainder is 0. So the last divisor 6 is the H.C.F. of 468 and 222 .
6 = 222 - 24 {tex}\times{/tex} 9
6 = 222 - (468 - 222 {tex}\times{/tex} 2) {tex}\times{/tex} 9 [Substituting 24 = 468 - 222 {tex}\times{/tex} 2]
6 = 222 - 468 × 9 + 222 {tex}\times{/tex} 18
6 = 222(1 + 18) - 468 × 9
6 = 222 {tex}\times{/tex} 19 - 468 {tex}\times{/tex} 9
6 = 468 × (-9) + 222 × 19
6 = 468x + 222y where x = - 9 and y = 19.
Hence, obtained.

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