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Published 1997 Revised 2021
Here is another method for testing divisibility by $7$ suggested by T.R.Mukundan
In step 1 of the method, we used the fact that there is a unique number in the $7$ times table (up to $10 \times 7 = 70$) ending in each digit $0$ to $9$. Is this true in other times tables? It works for $3, 7,9, 11\ldots$. But it certainly doesn't work for $2$ - no multiple of $2$ ends in $1$. It turns out that it works for any number not divisible by $2$ or $5$ (the prime factors of $10$). To understand why this is true, read this article on the Chinese Remainder Theorem.