Question

Express the H.C.F of no. 595 and 635 as a linear combination of 595 and 635 .

Answer 1

Answer:

HCF of 635 ,595 is x = 15 y = 16

Answer 2

$Given \: numbers \: 595 \:and \:635 .$

/* By applying Euclid's division lemma */

$635 = 595 \times 1 + 40 \: --(1)$

Since, Remainder ≠ 0, apply division lemma on divisor 595 and Remainder 40.

$595 = 40 \times 14 + 35 \: --(2)$

Since, Remainder ≠ 0, apply division lemma on divisor 40 and Remainder 35.

$40 = 35 \times 1 + 5\: ---(3)$

Since, Remainder ≠ 0, apply division lemma on divisor 35 and Remainder 5.

$35 = 5 \times 7 + 0\: ---(4)$

$\green { H.C.F = 5 }$

$Now, 5 = 40 - 35 \times 1 \: [From \: (3) ]$

$= 40 - ( 595 - 40 \times 14 ) \: [ From \: (2) ]$

$= 40 - 595 + 40 \times 14 \\= 40( 1 + 14 ) - 595 \\= 40 \times 15 - 595\\= ( 635 - 595 \times 1 ) \times 15 - 595 \: [ From \: (1) ]$

$= 635 \times 15 - 595 \times 15 - 595 \\= 635 - 595 ( 15 + 1 ) \\= 635\times 15 - 595 \times 16$

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