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10th Class Mathematics Real Numbers Question Bank MCQs - Real Number

  • question_answer
    If the HCF of 65 and 117 is expressible in the form 65m- 117, then find the value of m.

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: B

    Solution :

    By prime factorisation method, factors of 65 and 117 are given as,
                            \[65=5\times 13\]
     and                  \[117={{3}^{2}}\times 13\]
     \[\therefore \,\,\,HCF\left( 65,117 \right)=13\]              ... (i)
    According to the question, we have
    65m-117= HCF (65, 117)
    \[\Rightarrow 65m-117=13\]
    \[65m=13+117\]
    \[65m=130\]
    \[\Rightarrow m=2\]
     


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