What we old time Alaskans call Brown Bear, are what outsiders (and the hordes of carpet-baggers moving here) call Grizzly.
The idea of "physically stopping" a 800-900 pound bear which is running at 35-40 mph is impossible with a hand held firearm. (from a physics point of view. )
You can either kill them with a properly placed shot & properly constructed bullet combination,, or you can disable them by breaking a shoulder. The third option is wounding and pissing them off, that does not usually turn out so well for the rifleman.
In most villages the largest rifle you see is a 30-06. It is affordable, most folks are smaller stature, and they avoid getting into Brown Bear trouble with common sense. (you can't eat a brown bear anyway)
The closer you get to a large city or a big gun-shop, the larger the rifle calibers become.
Back when I hunted Browns, the largest bear I ever harvested was taken with a 7x57mm Mauser at 175 yards. (neck-spine shot). The worst case I had of wounding a bear which ran off and had to be tracked for two days, was when I gut-shot one with a 458 Win Mag at 40-50 yards.
This last fall I saw the remains of a 270 grain, 375-H&H Hornady factory load which fragmented after only penetrating 3 inches into a large brown bear.
I have never been charged by a bear unless I deserved it. While I no longer hunt them, I do carry a either my 350 Rem Mag, 416 Taylor or 45-70 when packing meat through Brown Bear prone areas. They read my mind and leave me alone. On the other hand my father and grandfather never owned anything larger than a 30-06 and they did just fine.