Rules of divisibility by 7,13,17,19

Its very easy rule to test for the divisibility by these numbers .
Divisibility rules for prime numbers 7,13,17,19 etc.
1. multiply last digit with multiplier.
2. Add or subtract this result from the remaining number.
3. Repeat the process until you get a number whose divisibility can be easily checked.


multiplier for various primes are as follows:
Prime number multiplier
7 -2
11 -1
13 +4
17 -5
19 +2
23 +7
29 +3
31 -3
37 -11
41 -4
43 +13
47 -14

Example: 826. Twice 6 is 12. So take 12 from the truncated 82.
Now 82-12=70. This is divisible by 7, so 826 is divisible by 7

Example: 19151--> 1915-1 = 1914 -->191 –4 = 187 --> 18-7 =11
so yes, 19151 is divisible by 11.

Example: 50661-->5066+4 = 5070-->507+0 = 507-->50+ 28 =78 and 78 is 6*13, so 50661 is divisible by 13.

Example: 3978-->397-5*8=357-->35-5*7=0. So 3978 is divisible by 17.

Example: 101156-->10115+2*6=10127-->1012+2*7=1026--102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

You can try for other prime numbers using multiplier.