# 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?

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:

We are given that 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. We need to find the maximum number of columns in which they can march.

Members in army = 616

Members in band = 32.

Therefore,

Maximum number of columns = H.C.F of 616 and 32.

By applying Euclidâ€™s division lemma

$616=32 \times 19+8$

$32=8 \times 4+0$

Therefore, H.C.F. = 8

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

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