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?

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 Euclid’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 .