Math, asked by ayaamkhan0741, 1 year ago

Find the HCF of 963 and 657 using euclid division lemma.

Answers

Answered by Anonymous
26

Using Euclid’s Division Lemma  

a = bq+r , o ≤ r < b  

963 = 657×1 + 306  

657 = 306×2 + 45  

306 = 45×6+36  

45 = 36×1+9  

36 = 9×4+0  

∴ HCF (657, 963) = 9.



Answered by Anonymous
199

Step-by-Step-explanation :-

By using Euclid's division algorithm (a = b × q + r)

Step 1 :

657) 963 ( 1

657

---------

306

963 = 657 × 1 + 306

Step 2 : As remainder is 306 which is not zero. so, now will take 306 as divisor and 657 as dividend.

306) 657 ( 2

612

--------

45

657 = 306 × 2 + 45

Step 3 : As remainder 45 which is not zero. Hence, now will take 45 as divisor and 306 as dividend.

45 ) 306 ( 6

270

--------

36

306 = 45 × 6 + 36

Step 4 : Now ,we consider the divisor 45 as dividend and the remainder 36 as divisor.

36) 45 ( 1

36

--------

9

45 = 36 × 1 + 9

Step 5 : Now ,we consider the divisor 36 as dividend and the remainder 9 as divisor.

9) 36 ( 4

36

--------

0

36 = 9 × 4 + 0

Finally , We get a remainder as 0.

Final Answer :-

Hence, H.C.F of ( 657, 963 ) is 9.

Additional Information :-

EUCLID'S DIVISION LEMMA

Euclid's Division Lemma states that for any two positive integers a and b, there exists unique integers q and r such that a = bq + r where r must satisfy 0 ≤ r < b

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