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word problems and turning them into algebraic equation to slove

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If sum of all digits in the number is divisible by 3 or 9, then the number is divisible by 3 or 9.  

(1.) 3,123,456
      3+1+2+3+4+5+6 = 24
     You can divide 24 by 3, but can't divide by 9, therefore 3,123,456 is divisible by 3, but not by 9.

If last digit of the number is even, then number is divisible by 2. 

(2.) 3,123,456
      6 is even number, therefore the given number is divisible by 2.
      6 / 2 = 3 ------> the given number is not divisible by 4, because 3 is odd number.

From (1.) and (2.) -----> the given number is divisible by 6

If last digit in the number 0 or 5, then number is divisible by 5. 

(3.) 3,123,456 is not divisible by 5.

Comments

3,123,456 is divisible by 4 because the rule for divisibility by 4 is as follows:
if the number formed by the two right-most digits is divisible by 4 then the original number is divisible by 4
56 is the number formed by the two right-most digits and 56/4=14

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