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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. The maximum number of columns in which they can march are ____

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Detailed Solution

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. The maximum number of columns in which they can march are 8.
Given is an army contingent of 616 members which is to march behind an army band of 32 members in a parade.
We have to find the H.C.F of both numbers using Euclid’s division algorithm.
According to Euclid’s division lemma, the relation of a and b is

a = b q + r

where a and b are positive integers, r = remainder and q = quotient.
Since 616 > 32, a = 616 and b = 32.
So,

616 = 32 × 19 + 8

.
Now, since the remainder is not 0,
a = 32 and b = 8

32 = 8 × 4 + 0

Remainder = 0
So, the divisor = H.C.F = 8.
Therefore, the maximum number of columns is 8.

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