Soap? I've never washed a patch yet....

Brushes wear out too...I replace them quite often, how much do them bore snakes cost?
Heres what I use...
Dewey's cleaning rod, caliber specific, I own a couple...
Dewey's Jag, wrap the patches around 'em, loops are a waste of money and time..
Shooter's Choice Solvent
Phospherous Bronze cleaning brushes, caliber specific
***Rod Guide, if you don't use one of these, throw the rest away, your wasting your time.
First off, what I do after an extended session of shooting, put the rod guide in, then push a brush wetted with Shooters Choice through the bore, till it extends all the way through, and of cource the gun is leaning forward so any excess solovent will not run into the action. As the brush is out of the muzzle, I wet it slightly again and pull it back through the barrel, till it is all the way back inside the bore guide.
What you don't want is to try and force the brush to go the other way, when the bristles are all leaning in the opposite direction. This might cause damage to your bore, and we don't want that.
Another lesson is to not try and win any races as you push the cleaning rod back and forth through your barrel.
In and Out is "1", do this at least 10 times, then go do something else for a while, load some rounds, read a book, it doesn't matter, just let that solvent do its job. If you don't have time, continue....
Run a patch through, notice the "blue", thats copper, the black crud is powder fouling. Run patches till dry, this should only take a couple. Now repeat the above steps, and brush it again 10 times.
Clean-Patch till patches come out clean. You'll be surprised how dirty your barrel was when you "thought" you were cleaning it before.
When all done, your barrel will be down to bare metal, and there will be nothing in there to protect it from the elements. If its going in the safe, I'll wet a patch with oil, and run it through it for protection, if its going in the field, I'll oil it, then dry patch it for excess oil, don't want any "pressure" signs on my brass because of forgetfullness.
Now, I didn't get into action or bolt cleaning, this is just how I clean my barrels.
Tell you one thing though, you sure will learn fast what barrels you own are "Rough". Damn things will either take forever to get clean....or just "won't".
Picked up a Smith & Wesson 1500 (yep, a Howa) for my Dad, after 120-something patches, with scrubbing in between, I never got a clean patch out of it....might want to try Tubb's "Final-Finish" on that thing...sure woudln't hurt!