Divisibility Rules

Divisibility Tricks, numberphile (youtube)

Divider - Check
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2 - even

3 - digit sum div by 3, eg 162 = 1+6+2 = 9

4 - last two digits div by 4 (because 1000 = 4m)

5 - last digit = 5 or 0

6 - even and div by 3

7 - hard
eg 6,976,984 => 984 - 976 + 6 = 14 div by 7
eg 872,123 => 123 - 872 = -749
for three-digit 749 => 74 - 2*9 = 56 div by 7


8 - last three digits div by 8
for three-digit num, eg 464 => 2*46 + 4 = 96 div by 8

9 - digit sum div by 9

10 - last digit = 0

11 - reverse, cross sum of digits div by 11,
eg 5025669 => 9665205 => 9-6+6-5+2-0+5 = 11

12 - div by both 3 and 4


* Numbers ending with 1,3,7,9 div by N
eg 1053 div by 23?
23 => 69 (any multiple ending with 9) => 69 + 1 = 70 gives m = 7
1053 = 10 t + q, where t=103, q=5
m q + t = 7*5 + 103 = 138 div by m.
Then 1053 is div by 23