The most constrained clues are the two 7s in the corners. A prime number like 7 can only form a 1x7 or 7x1 rectangle. The Purple 7 in the top-right corner cannot be a 7x1 vertical strip, as it would collide with the bottom of the grid. It must be a 1x7 horizontal strip. This solves the top row.

Similarly, the Pink 7 in the bottom-right corner cannot be a 1x7 horizontal strip (it would hit the left edge). It must be a 1x7 vertical strip, solving the right-most column.

The placement of these two strips creates a chain reaction. With the entire right column now occupied by the Pink 7, the Blue 4 clue next to it is forced. It becomes part of a 2x2 square, also containing the dark grey block, as this is the only way to satisfy a 4-area shape in that confined space.

The Blue 8 in the top-left corner now has its horizontal expansion blocked by the Purple 7's strip. It can no longer be an 8x1 rectangle. Its only remaining logical shape is a 1x8 vertical strip, locking down the entire left edge.

This forces the Gold 3 to become a 1x3 strip right beside it.

With the outer frame largely defined, the inner pieces fall into place. The Brown 6 on the bottom is now boxed in by the Blue 8 and Pink 7 strips. It has only 7 cells of width to work with, forcing it into a 6x1 horizontal shape.