43. DIVISIBILITY TESTS
 
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Pick-up the technique

1. Test for 3
Add the digits; Repeat till get single digit; Test by 3.

2. Test for 7
Subtract 2 times units digit from rest of number;
Repeat until you get a small enough number; Test by 7.

3. Test for 11
Sum of odd-place digits & sum of even-place digits differ by multiple of 11 (0, 11, 22, ...).

4. Test for 13
Add 4 times units digit to rest of the number;
Repeat if needed; Test by 13.
We shall denote Test for 7 above as '- 2 x units'
We shall denote Test for 13 above as '+ 4 x units'
More divisibility tests, using this notation,
for 17, 19, 23, ... follow.