Any 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?

Explanation

The maximum number of columns is the H.C.F. of 616 and 32.
Using Euclid's division algorithm
616- 32 `xx 19 + 8`
` 32 = 8 xx 4 + 0`
`therefore " " ` H.C.F. (616 , 32) = 8 `" " (because` remainder = `0 implies` recent divisor is H.C.F.)
Hence , the maximum number of columns = 8