DIVISIBILITY BY TWELVE :
Rule : Any number which is divisible by both 4 and 3, is also divisible
To check the divisibility by 12, we
(1) first divide the last two-digit number by 4. If it is not divisible by 4,
the number is not divisible by 12. If it is divisible by 4 then
(2) check whether the number is divisible by 3 or not.
Ex.1. 135792 : 92 is divisible by 4 and also (1+3+5+7+9+2=)27
is divisible by 3 ; hence the number is divisible by 12.
Remark : Recall the method for calculation of digit-sum. What did you
do earlier "Forget nine". Do the same here. For example:
digit-sum of 135792__1 plus 3 plus 5 is 9, forget it. 7 plus 2 is 9, forget
it. And finally we get nothing. That means all the "forget nine" counts a
number which is multiple of 9. Thus, the number is divisible by 9.
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