An Army Contingent of 616 Members and an Army Band of 32 Members Marching in Columns

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: 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?

Step 1: Identify the Mathematical Concept

The maximum number of columns in which both groups can march is given by the HCF (Highest Common Factor) of 616 and 32.

Step 2: Use Euclid’s Division Algorithm

616 = 32 × 19 + 8

Since the remainder is not zero, apply the algorithm again.

32 = 8 × 4 + 0

Since the remainder is zero,

∴ HCF (616, 32) = 8

Final Answer

∴ The maximum number of columns in which both the army contingent and the army band can march is 8.

Conclusion

Thus, by using Euclid’s division algorithm, we find that the maximum number of columns possible is 8.