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An army contingent of 616 members is to march behind an army band of 32 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?

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#### Solution

For the above problem, the maximum number of coulmns would be the HCF of 616 and 32

We can find the HCF of 616 and 32 by using Euclid Division algorithm.

Therefore

616 = 19 x 32 + 8

32 = 4 x 8 + 0

8 = 8 x 1 + 0

Therefore HCF (616, 32) = HCF of (32, 8) = 8

Therefore the maximum number of columns in which they can march is 8

Concept: Euclid’s Division Lemma

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