Find the hcf of 657, 963 by euclid division algoritham method?

Question

Find the hcf of 657, 963 by euclid division algoritham method?

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Iris 8 months 2021-10-03T08:41:22+00:00 2 Answers 0 views 0

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    0
    2021-10-03T08:42:56+00:00

    Given:- Two numbers i.e. 657 and 963.

    To Find:– The HCF of 657 & 963 by the Euclid division algorithm.

    Solⁿ:- We know the Euclid division algorithm is expressed in the form:

    a = b \times q + r

    where a= Dividend , b= divisior , q= quotient and r= remainder.

    Now,

    →963= 657 × 1 + 306

    →657=306 ×2 +45

    →306=45 ×6 +36

    →45= 36 ×1 +9

    →36= 9 ×4 +0

    Thus, HCF of 657 & 963 is 9.

    0
    2021-10-03T08:43:03+00:00

    ★ 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.

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

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