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

` 616 = 32xx 19+ 8`
`rArr r = 8 ne 0`
`32 = 8 x 4+0`
`rArr r =0`
The HCF of 32 and 616 is 8.

In `Delta OPA and Delta OPB`
`anglePAO = angle PBO` (each `90^(@)`)
OP = OP ( common)
OA = OB (radii of same circle)
`" " Delta OPA ~= Delta OPB `( by RHS congruency axiom
Hence PA = PB (CPCT)