word problems and turning them into algebraic equation to slove

Question

Using divisibility tests determine if 3,123,456  is divisible by:

 

3?

 

4?

 

5?

 

6?

 

9?

 

yes or no and how do you know based on divisibility rules?

Answer 1

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.