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# A group of 616 students is to march behind an army band of 32 members in a parade. The two groups must march in the same number of columns. What can be the maximum number of columns in which they march?81243

A
8
B
4
C
12
D
3
Solution
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#### It is given that there is a group of 616 students march behind an army band of 32 members in a parade. We use euclid's algorithm in this problem.Let us first state Euclid’s division algorithm:To obtain the HCF of two positive integers, say c and d, with c>d, follow the steps below: Step 1 : Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and r such that c=dq+r,0≤r<d. Step 2 : If r=0, d is the HCF of c and d. If r≠0, apply the division lemma to d and r. Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be the required HCF. Now, let us apply the Euclid’s division algorithm to 616 and 32 as follows:616=32×19+8Since the remainder is 8 which is not equal to 0. Therefore, we again apply Euclid’s division algorithm to 32 and 8 as shown below:32=8×4+0Since the remainder is 0, therefore, the HCF of 616 and 32 is 8.Hence, the maximum number of columns in which they march is 8 columns.

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