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Any contingent of 616 members is to m...

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?

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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
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