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- 8
- 12
- 4
- 3

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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+8

Since 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+0

Since 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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