MathematicsAn army contingent of 1000 members is to march behind an army band of 56 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

An army contingent of 1000 members is to march behind an army band of 56 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?


  1. A
    8
  2. B
    9
  3. C
    12
  4. D
    10 

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    Solution:

    Given that the number of members in the army contingent is 1000 and the number of people in the army band is 56.
    The maximum number of columns is equal to the HCF of 1000 and 56.
    Write down the prime factorization of 1000 and 56.
    ⇒1000=2×500 ⇒1000=2×2×250 ⇒1000=2×2×2×125 ⇒1000=2×2×2×5×5×5 ⇒56=2×28 ⇒56=2×2×14 ⇒56=2×2×2×7  
    Since HCF of 1000 and 56 is 2×2×2=8  ,
    Hence, the maximum number of columns in which the two groups march is 8.
    Therefore, the correct answer is option (1).
     
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