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Use Euclid’s division algorithm to find the HCF of {210}{{and}

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Use Euclid’s division algorithm to find the HCF of $210 and 55$ .

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Text solutionVerified

Solution:

210 = 55 \cdot 3 + 45

55 = 45 \cdot 1 + 10

45 = 10 \cdot 4 + 5

10 = 5 \cdot 2 + 0

H C F = 5

on back calculating--

5 = 45 - 10 \cdot 4

5 = 45 - (55 - 45) \cdot 4

5 = 45 \cdot 5 - 55 \cdot 4

5 = (210 - 55 \cdot 3) \cdot 5 - 55 \cdot 4

5 = 210 \cdot 5 - 55 \cdot 15 - 55 \cdot 4

5 = 210 \cdot 5 + 55 \cdot (- 19)

5 = 210 \cdot x + 55 \cdot y

x = 5, y = - 19

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Question Text	Use Euclid’s division algorithm to find the HCF of $210 and 55$ .
Answer Type	Text solution:1
Upvotes	150