Here is an interesting article that tested ten homemade grout cleaners: https://brendid.com/ultimate-guide-t...rout-and-tile/
The following recipe was her favorite:
Mix together 1/2 cup of baking soda, 1/4 cup of hydrogen peroxide, and 1 tsp dish soap. Apply cleaning mixture onto grout, wait 5-10 minutes, scrub and rinse.
Bob Vila recommends the same mixture: https://www.bobvila.com/articles/hom...grout-cleaner/
A grout brush with a handle will keep you off of your knees when scrubbing. It would make the job easier when cleaning a large area:
https://smile.amazon.com/Grout-Brush...ct_top?ie=UTF8