What is the part of speech of quantifiers? Adjective or determiner?

Question

Quantifiers are adjectives and adjectival phrases that give approximate or specific answers to the questions "How much?" and "How many?" Education First

We use the quantifiers much, many, a lot of, lots of to talk about quantities, amounts and degree. We can use them with a noun (as a determiner) or without a noun (as a pronoun). Cambridge Dictionary

What is the part of speech of "quantifiers"? Are they adjectives or determiner? Or both together?

Answer 1

There is no universal convention on the parts of speech in English, except perhaps that linguists dislike the term part of speech (they prefer terms like lexical category or word class). Consider the following:

• Under the traditional model, as for example given in Joseph Priestly's 1761 The Rudiments of English Grammar, every word in a sentence could supposedly be classified as one of exactly eight types: noun, pronoun, verb, adjective, adverb, conjunction, preposition, or interjection. This model is deprecated by linguists, but still widely taught.
• The magisterial 2002 Cambridge Grammar of the English Language (CGEL), by Rodney Huddleston and Geoffrey Pullum, divides conjunctions into two classes as well as elevates the derminer, giving noun, verb, adjective, adverb, preposition, determinative, subordinator, coordinator, and interjection as the word classes.
• Dave Willis, co-author of the Collins COBUILD English Course, uses noun, verb, adjective, adverb, preposition, determiner, quantifier, and conjunction.
• The Routledge English Grammar by Roger Berry lists noun, adjective, adverb, (main) verb, pronoun, determiner, preposition, auxiliary verb, and conjunction.

The case has been made that determiners should be considered a separate class of words, just as pronouns are distinct from nouns. After all, it is a closed set of words which behaves differently from adjectives: they cannot be stacked, they cannot be graded, they cannot be intensified. They have a distinctive purpose in a sentence. Modern textbooks seem to agree, including all three noted above. Note that the Education First website also recognizes this distinction in the organization of its site.