Question

use euclids division algorithm to find the hcf of 286 and 854​

Answer 1

Answer:

854 = 286 × 2 + 282

286 = 282 × 1 + 4

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

Know More:

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