How do I clean filthy grout on an old bathroom floor?

Here is a great video tutorial for cleaning grout for you: https://www.youtube.com/watch?v=nbOU5UZNsa0

I used Lysol toilet bowl cleaner in the Black squirt bottle and it worked well.

Here is a recipe for homemade grout cleaner: https://www.hometalk.com/diy/clean/floors/homemade-grout-cleaner-recipe-41693881

Homemade Grout Cleaner Recipe

Try making a paste of OxyClean with a little water. Use a toothbrush to scrub. Be sure to seal when dry!.

Hell. These links may be helpful.

https://www.hometalk.com/diy/clean/bathroom/the-best-way-to-clean-grout-ever-2295735?expand_all_questions=1

https://www.hometalk.com/diy/clean/floors/homemade-grout-cleaner-recipe-41693881?expand_all_questions=1

https://www.bobvila.com/articles/cleaning-grout/#.Wi6YzKZOmf0

https://www.hometalk.com/search/posts?filter=clean%20grout

Additionally

Painted Tile Grout Refresh with grout pen

https://www.blesserhouse.com/painted-tile-grout-refresh/

Finally-Grout cleaning and grout removal and replacement Hope this helps

https://www.hometalk.com/diy/clean/bathroom/how-to-clean-grout-and-install-new-grout-that-won-t-stain-23803774

I like bar keepers friend and a good stiff grout brush. If the grout is white, you can use some bleach, too. If it's clean but stained to look dirty, you can use a grout stain or paint to change and even out the color. After you get the grout the way you want it, make sure to seal it to make cleaning easier in the future. Sealing it once or twice a year is best.