Why are the words hundred, thousand, million, and trillion singular after plural numbers?

Can anyone give a grammatical explanation why the words hundred, thousand, million, and trillion are singular after plural numbers?

For example, why can't we say three hundreds or 4 thousands or five millions, etc?

One of my students asked me and all I could say is that it is an exception to the rule of bringing a plural word after a plural number!

Solution 1:

This phenomenon - the uninflected plural of numerals - is a remnant of Old English. In Old English, words like hund "hundred" and þusend "thousand" were indeclinable. That is, they did not change form based on case or number.

Today this remains but only in some limited situations - specifically, when the number word is preceded by a determiner (a, one, another number). This is also the case in English's sister language Frisian (you knew English had a sister language, right?), where tûzen, etc., don't take a plural form.

Solution 2:

I've always thought that when the words hundred, thousand, million and trillion are used after a specific number, they are part of that number. I know that number fifteen, for example, signifies the plural form of the noun that follows, but there's no need to pluralise the word fifteen. Similarly, it looks logical to me not to pluralise the words that form the number. So two hundred and the like is ruled by this logic. Note that the same thing happens with the (less frequent) words dozen and score.

When the number is not specific and you want to talk about a few hundreds of people, for example, you then pluralise hundred because you aren't naming a specific number. This is the case when the non-specific number is followed by the preposition of. If you say a few hundred people, where no preposition intervenes, then hundred behaves in the same way as when the number is specified. A possible explanation for this could be that it follows the rule that forms two hundred because the construct is the same, while the use of the preposition of changes things.