Agardener has 27 pansies and 36 daisies. he plants an equal number of each type of flower in each row. what is the greatest possible number of pansies in each row?

There are 27 pansies.
The factors of 27 are (3,9)
Therefore,
Either (a) plant 3 pansies in 9 rows, or
           (b) plant 9 pansies in 3 rows.

There are 36 daisies.
The factors of  36 are (3,12), (6,6) or (9,4).
Therefore
Either (a)  plant 3 daisies in 12 rows, or
           (b) plant 12 daisies in 3 rows, or
           (c) plant 6  daisies in 6 rows, or
           (d) plant 9 daisies in 4 rows, or
           (e) plant 4 daisies in 9 rows.

Because each row has an equal number of pansies and daisies, the only common arrangements are
(a) 9 pansies and  12 daisies in 3 rows, or
(b) 3 pansies and 4 daisies in 9 rows.

To have the greatest number of daisies in each row means planting 9 pansies and 12 daisies in 3 rows.

 
The greatest number of pansies per row is 9.
Plant 9 pansies and 12 daisies in 3 rows.