[Stratoscope]

Perhaps it is some kind of regional difference. I've always lived on the US West Coast, and I've heard "divide four by two" expressed as "divide two into four" many times - and never the other way around.

I never use the "into" phrasing myself because it is confusing to me. But it does make some kind of sense if you think about it this way: "How many twos can you put into four?"

[Crito]

To me, "divide A into B" sounds like a some sort of anachronism that you might find in a 17th century one-room schoolhouse, while "divide B by A" sounds perfectly natural.

I went to school on the US East Coast, so you might be onto something here.