Q. 44.7( 3 Votes )

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?

Answer :

This question is based on Euclid's Division Lemma,

Given positive integers a and b, there exist a unique integers q and r satisfying


a = bq + r ,


Where 0 ≤ r ≤ b.


According to the question,


Members in army contingent = 1000


Members in army band = 56


To find a maximum number of columns to march behind army band in the same number of columns, we have to find HCF of 1000 and 56.


1000 = 56 × 17 + 48


56 = 48 × 1 + 8


48 = 8 × 6 + 0


The remainder has become zero, so our procedure stops.


Since the divisor at this stage is 8.


HCF (1000 , 56) = 8


Required columns = HCF (1000 , 56) = 8


Hence, the maximum number of columns in which they can march is 8.


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