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?

HCF (616,32) is the maximum number of columns in which they can march.
Step 1: First find which integer is larger.
616 > 32
Step 2: Then apply the Euclid's division algorithm to 616 and 32 to obtain
616 = 32 × 19 + 8
Repeat the above step until you will get remainder as zero.
Step 3: Now consider the divisor 32 and the remainder 8, and apply the division lemma to get
32 = 8 × 4 + 0
Since the remainder is zero, we cannot proceed further.
Step 4: Hence the divisor at the last process is 8
So, the H.C.F. of 616 and 32 is 8.
Therefore, 8 is the maximum number of columns in which they can march.