# 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.