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?

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.