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 :

To find the maximum number of columns, we have to find the H.C.F. of 616 and 32

i.e. 616 = 32 \(\times\) 19 + 8

and 32 = 8 \(\times\) 4 + 0

\(\therefore\) H.C.F of 616 and 32 is 8.

Hence, maximum number of columns is 8.