Which form is correct?
None of A,B or C divides X
None of A,B and C divides X
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Let's get real. [joke]
There are many shortcuts or tricks that allow you to test whether a number, or dividend, is divisible by a given divisor. This page focuses on the most-frequently studied divisibility rules which involve divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and by 11
Finally, none of refers to a portion of something. Numbers here are not portions. They are whole numbers.
We would never say in English: None of 5, 10 or 3 etc.
Why? Because it would imply that 5 can be broken down into portions. It can't. It can only be rewritten with other whole numbers: 2+ 2+1 is 5.
AS IN: None of the pie or pies were left after the party. The guests had eaten the whole thing or all of them.
Neither form is desirable. They are hard to understand. Generally starting a sentence with None of and then iterating a list of items to which None of applies is cumbersome. For example, None of my kids, Carol's kids, or Lester's kids swim well. If none of them swim well you don't need to specifically call out the none. I will understand that from context.
My kids, Carol's kids, and Lester's kids do not swim well.
That means none swim well.
A, B, and C do not divide X.
Once again that means none. No reason to say it.
For sentences with a single subject none of works very well.
None of our kids swim well.
None of those numbers divide X.
It's when you add the itemized list to none of that things start getting cumbersome.