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?

Answer 1

Maximum number of columns which is common to both the groups $=HCF(616,32)$

$616=(32\times 19)+8$
$32=(8\times 4)+0$
Remainder in this case is zero.
$\therefore HCF(616,32)=8$
Hence, the maximum number of columns$=8$