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Not being a multiple 10 was handled effectively by the negated number theoretic congruence(triple bar) relation. Problem was made relatively simple by showing, in a modular arithmetic fashion that each of the 2022 factors, represented by PI Product notion, is not a multiple of 5. This saved an immense/undoable amount of arithmetic computation!
Similar but also different was the Proof of obtaining a multiple of 10 by using only the four arithmetic operations on three arbitrary integers. This was nicely demonstrated by Carlton Banks, November 2017, at math stack exchange.
Proving Product Of 2022 Factors is Not A Multiple Of 10