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Divisibility rules (base 10)

A number is divisible by 2 if the last digit is even.

A number is divisible by 3 if the sum of the digits is divible by 3 (465 = 4+6+5 = 15; 15/3 = 5 therefore 465/3? is true.

A number is divisible by 4 if the last two digits are divisible by 4 (728; 28 is divisible by 4)

5: if the last digit is either a 0 or 5

6: if the number is divible by both 2 and 3.

7: this one I had to play around with before I could recall it:

a) double the units digit

b) subtract that from the remaining digits

c) if the difference is divisible by 7 then original number is divisible by 7. If the result is not readily apparent - continue steps a and b until number is/not divisible by 7. For example: 2884

288 - (2*4) = 280, okay bad choice (to easy) 280 = 7 * 40.

Trying 3562: 356 - 4 = 352 (nope 50 * 7 is 350, so not divisible).

8: if last 3 digits are divisible by 8 (ie. 1064 or 2160)

9: if sum of the digits is divisble by 9 (64,593 is 6+4+5+9+3= 27 so 64,593 is divisible by 9.

10: if the last digit of the number is a 0.

11: another *strange* one! if the sum of the odd digits (by place in the number) subtracted by the even number digits is divisible by 11 ! 49731 is (4 + 7 + 1) - (9 + 3) = 12 - 12 = 0 (0 evaluates to true) so true. 135916 is (3 + 9 + 6) - (1 + 5 + 1) = 18 - 7 = 11, so true.

That's all I remember but maybe 12 is true if # is divisible by 3 and 4. Hmmm, 144 fits. 156 works. 324? yep. Just adding 12 in my head going up to 408 - each one of those worked for 3 and 4 .

13? Forget about it!