Question

Using Euclid's division algorithm, find the HCF of 231 and 297. Also, check the numbers are co-prime or not.​

Answer 1

Given :- Using Euclid's division algorithm, find the HCF of 231 and 297. Also, check the numbers are co-prime or not. ?

Answer :-

we know that, Euclid's division Lemma states that for any two positive integers a and b there exist two unique whole numbers q and r such that :-

• a = bq + r, where 0 ≤ r < b.

Here,

• a = Dividend.
• b = Divisor.
• q = Quotient.
• r = Remainder.
• The values r can take = 0 ≤ r < b.

so, using Euclid's division algorithm we get,

→ 297 = 231 * 1 + 66

→ 231 = 66 * 3 + 33

→ 66 = 33 * 2 + 0

since remainder becomes zero . { r = 0 .}

therefore, we can conclude that, the HCF of 231 and 297 is 33 .

and, since they have factors 33 other than 1, given number are not co - prime numbers .

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Answer 2

Given:

Using Euclid's division algorithm, find the HCF of 231 and 297. Also, check the numbers are co-prime or not.

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 231 and 297 by using Euclid’s division algorithm:

297 = 231 x 1 + 66

• The Remainder is not equal to 0, So apply the division lemma on 231 

231 = 66 x 3 + 33

• The Remainder is not equal to 0, So apply the same method on 66.

66 = 33 x 2 + 0

• The Remainder is equal to 0.

Hence, By using Euclid’s division algorithm the HCF of 231 and 297 is 33

Both the numbers 231 and 297 have the common factor 33. hence they are not co-prime numbers.

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