MathematicsIf the HCF of 657 and 963 is expressible in the form 657x+963×(-15), find x.

If the HCF of 657 and 963 is expressible in the form 657x+963×(-15), find x.

  1. A
    10
  2. B
    15
  3. C
    20
  4. D
    22 

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    Solution:

    The given numbers are 657 and 963.
    Euclid's Division Lemma states that, if two positive integers “a” and “b”, then there exists unique integers “q” and “r” such that which satisfies the condition:
    a=bq+r where 0≤r≤b
    Calculation of HCF using Euclid’s division algorithm is as follows:
    963=657×1+306
    ⇒657=306×2+45
    ⇒306=45×6+36
    ⇒45=36×1+9
    ⇒36=9×4+0
    ⇒HCF(657,963)=9
    Calculate x.
    HCF=657x+963×(-15)
    9=657x+963×(-15)
    ⇒9=657x-14445
    ⇒657x=14445+9
    ⇒657x=14454
    ⇒x=14454657
    ⇒x=22
    Therefore, if the HCF of 657 and 963 is expressible in the form 657x+963×(-15) then the value of x is 22.
    Hence, option 4 is correct.
     

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