Scanned documents are the most compressible PDFs of all — because every page is a photograph of paper. That also makes them the easiest to ruin if you over-compress. Here's how to get a small, still-readable file.
Why scanned PDFs are so big
A scanner captures each page as a high-resolution image. A colour scan at 600 DPI can be several megabytes per page. The text isn't 'text' to the computer — it's pixels — which is why scanned PDFs aren't searchable until you run OCR.
How to shrink them safely
Downsample the page images to around 150 DPI and re-encode them at a moderate JPEG quality. This usually keeps text clearly legible while cutting size enormously. Convert to grayscale if colour isn't needed.
Make it searchable too
If you need to search or copy text from a scan, run OCR (optical character recognition) to add a text layer. This is separate from compression but often wanted at the same time.