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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?

Answer:

**Solutions: Given, number of army contingent members = 616**

**Number of army band members = 32**

**If the two groups have to march in the same column, we have to find out the highest common factor between the two groups. **

**HCF (616, 32) gives the maximum number of columns in which they can march.**

**By using Euclid’s algorithm to find their HCF, we get,**

**Solutions: Given, number of army contingent members = 616**

**Number of army band members = 32**

**If the two groups have to march in the same column, we have to find out the highest common factor between the two groups. **

**HCF (616, 32) gives the maximum number of columns in which they can march.**

**By using Euclid’s algorithm to find their HCF, we get,**

**Since, 616 is greater than 32, therefore,**

**616 = 32 × 19 + 8**

**Since, remainder 8 ≠ 0, **

**We consider new dividend 32 and new divisor 8, and again using Euclid’s division lemma, we get,**

**32 = 8 × 4 + 0**

**Now we have got a remainder as 0. Since the divisor at this stage is 8. Therefore, HCF (616, 32) = 8.**

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

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