Question

Use Euclid’s division algorithm to find the HCF of ii. 286 and 854

Answer 1

Answer :-

using Euclid’s division algorithm we get,

286 ) 854 (2

-572

282 ) 286 (1

-282

4 ) 282 ( 70

-280

2 ) 4 ( 2

-4

0

therefore, we can conclude that, HCF of 286 and 854 is 2 .

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Answer 2

Given:

Use Euclid’s division algorithm to find the HCF of 286 and 854

Solution:

Euclid Division Algorithm:  

• Two positive integers 'a' and 'b' there exits two unique integers 'q' and 'r' satisfies a=bq+r where 0 ≤ r ≤ b.
• According to Euclid Division Algorithm: Dividend = Divisor x Quotient + Remainder

Finding HCF of 286 and 854 by using Euclid’s division algorithm:

854 = 286 x 2 + 282.  

• The Remainder is not equal to 0, So apply the division lemma on 286.  

286 = 282 x 1 + 4.  

• The Remainder is not equal to 0, So apply the same method on 282.

282 = 4 x 70 + 2

• The Remainder is not equal to 0, So apply the same method on 4.

4 = 2 x 2 + 0

• Remainder is equal to 0.

Hence, By using Euclid’s division algorithm the HCF of  286 and 854 is 2

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