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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?

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

Step 1: First find which integer is larger.

616>32

Step 2: Then apply the Euclid's division algorithm to 616 and 32 to obtain

616=32×19+8

Repeat the above step until you will get remainder as zero.

Step 3: Now consider the divisor 32 and the remainder 8, and apply the division lemma to get

32=8×4+0

Since the remainder is zero, we cannot proceed further.

Step 4: Hence the divisor at the last process is 8

So, the H.C.F. of 616 and 32 is 8.

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

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