Just follow the directions on remingtons website. Every gun is totally different and has to be treated as such. If you fire a round and clean (with a heavy copper cutting solution), and its very coppered, then you have you to keep firing and cleaning until you see that fall off. Could be 3 rounds, could be 20.

One thing I do is use JB's to semi lap the bore before even firing. Its worked for me for a long time. I run JB's thru 200 strokes before a shot is fired. Some will say yoru wearing down your rifling, but it would take 5000 stokes even to think about premature wear. This is an optional step that helps the breakin go much faster.

My sako recently for instance, I fired a round, then cleaned, and did this 3 rounds. By the third round, I had very little copper/fouling. So I started shooting 3 rounds and cleaning. By the 4th set of 3 round shots, I have very little copper. I moved up to 10 rounds. I did this for two sets, and figured that was a enough. A very easy rifle to breakin. Some remingtons however I have had in 300RUM, I cleaned every round for 20 shots, and still the 20th was as bad as the 2nd. It was a very rough barrel. And no amount of breakin was changing that. It never did smooth out in 600 rounds.

Remember there is no set rules. every gun is different.