The most logical starting point is the top-left corner. The Purple 2 clue, being on the top edge, must be a 2x1 rectangle. A 1x2 vertical piece would not align with the edge clue. This placement immediately constrains the top-right corner. The Green 4 must fill the remaining top row, making it a 4x1 rectangle. Any other configuration (like a 2x2 square) would not fit. With two simple moves, the entire top row is solved.

With the top-left corner occupied by the 2x1 Purple piece, the Teal 10 on the left edge has a remaining height of 5 squares. The only factors of 10 that fit are 2x5 or 5x2. To fit in the remaining space, it must be a 2x5 rectangle. This single move solves the entire left side of the grid.

This is the critical step. Solving the top and left sides leaves a 4x5 rectangle to be solved. More importantly, it creates two distinct vertical zones: A 1-wide column (column 3) next to the Teal 10.

A 3-wide column (columns 4-6) for everything else.

The visual hints for the central pieces now become invaluable. The Orange and Red pieces are clearly tall and thin, while Yellow and Blue are wide. The thin Orange and Red pieces must therefore occupy the 1-wide column. The solved grid reveals they are 1x3 and 1x2, filling the 5-unit height of that column.

This forces the wide Yellow, Blue, and the corner Brown 6 pieces into the 3-wide column. The only way for the Brown 6 to fit in a 3-wide column is to be a 3x2 rectangle. A 2x3 orientation would be too narrow.