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According to WordHippo:

The noun core can be countable or uncountable.

In more general, commonly used, contexts, the plural form will also be core.

However, in more specific contexts, the plural form can also be cores e.g. in reference to various types of cores or a collection of cores.

But doesn't it seem that in the general case the word actually is uncountable? Merriam-Webster or Oxford dictionaries don't say anything about its plural form.

Another point: Google Ngram shows that "to their core" is used more than "to their cores" 38 times. Does this mean that "core" in this case is not specific? But the word "their" indicates that the context is specific.

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    Why the downvote? Because the question relies on the spurious authority of WordHippo when there are many far more reliable sources of information available on the internet. Merriam Webster. Cambridge. Oxford. Longmans. Collins. etc – Tᴚoɯɐuo May 9 '18 at 13:34
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    This discussion has been moved to chat. If you'd like to continue the discussion, please use the chat room or see the related meta question: Why should question contain incorrect source be downvoted? – snailcar May 12 '18 at 17:48
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Literally, the word core refers to things inside a 3D structure (fruit, planets, etc). Figuratively, core has the notion of the thing or value etc that is 'central' or 'most important'. When used in the figurative sense (and in relation to a plurality of individuals, not just one individual), the term is conventionally used when there is one value or principle or 'heart' etc that is common to the whole group. In a sense, it wouldn't be 'core' if there were more than one of those things.

If core is used as a modifier (e.g. core activities - see below), then the word core is properly used in its base form, regardless of the number of (say) activities are involved.

core noun The part of something that is central to its existence or character. ‘the plan has the interests of children at its core’ (as modifier) ‘managers can concentrate on their core activities’ - ODO

I'm not familiar with how WordHippo is set up. In particular, I don't know whether this is crowd-sourced information at one extreme or whether it is curated by a panel of experts at the other. The entry you link to has no examples of what it means by "the plural form will also be core", so I can't tell you what they were referring to. At a guess, they might have been referring to the 'modifier' sense in the dictionary example above.

The Ngram link you provided (and clicking through to "to their core") does have examples, though, so I'll comment on a few here:

Many people had found their refuge here; many people had connected to their heart and to their core here. - Four Sides to the Core

The terms heart and core are used in the uncountable sense of 'basic value'. You can compare this with, say, "found their love" (uncountable) and contrast it with, say, "found their hobbies" (countable).

I started a journey toward stripping the standards to get to their core. - The Core Deconstructed

This uses the term core in the 'collective most important bit' sense, hence the use of the singular. It can alternatively be read as a figurative use, which justifies using the base case.

Following this line of thinking, Chauncey Billups and Chris Bosh are both exceptional NBA basketball players, but they have unique, individualized needs relating to their core functionality. - Conditioning to the Core

This uses the term core in the modifier sense (one noun modifying another), which justifies using the base case.

Note that the term core is not used in a plural sense in any of the above examples.

The "to their cores" click-through from your Ngram link does show some examples of cores used in the plural sense. Glancing at a few examples, it seems that in each case they refer to different 'cores' (e.g. one 'main thing' per company, not a unifying 'main thing' for the collection of companies), whether literal or figurative. The chart from your Ngram link shows that this usage appears less often than the singular or base case "to their core" (at least, in Ngram's database).

In any case, contrary to WordHippo's assertion, the examples above support the notion that the term core isn't used in the 'singular' to indicate the plural.

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    Good answer, especially the comparison with other abstract concepts like love. There are many nouns that fall into this category and have similar behavior. – Andrew May 9 '18 at 16:35

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