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    why is a number divisible by 3 if its digit sum is divisable by 3?

    +1  Views: 928 Answers: 4 Posted: 10 years ago
    mycatsmom

    What's a " digit sum '' ?
    Bob/PKB

    A digit sum is adding the number in the digit. For example, if you say 963 is divisible by 3, you "prove it" by adding the digits in 963...9 + 6 + 3, which = 18. Then you add 1 + 8 = 9, and 9 is divisible by 3. You could stop at 18, but the point is to reduce the digit sum as much as possible, to go with your divisor, of course.
    An even number divisible by 3 (966, for example), is also divisible by 6, BECAUSE 2 and 3 are factors of 6.

    4 Answers

    The number three rule!

    mycatsmom

    What is the number 3 rule ?

    ""


     


     

    mycatsmom

    Thank you, Chelleanne
    Bob/PKB

    RE: 4 : If the last TWO digits form a number divisible by 4; In 12,348, 48 is divisible by 4 (12). In 1,234, 34 is NOT evenly divisible by 4. Part of the explanation is missing from your answer chart. This is a wonderful chart. Teachers should teach math tricks whenever they can.

    It is one of the neat things about math!  Knowing the "rules" Chelleanne posted can help you get through some timed math tests quickly.  There is a trick for multiplying by 11, too.  I have a book called "Rapid Math Tricks" and it's nice to pull a trick out once in awhile and amaze and astound family and friends.  

    2 goes into even numbers, 3 goes into anything totaling a number divisible by three, 4 goes into anything that ends with 4 number divisible by four (I’m trying to remember the rule for 4).  You should study Trachtenberg math. With it you can add, multiply, square root, etc. in a matter of seconds.  19 digit numbers X 18 digit numbers in seconds!!!!! Check him here:  http://en.wikipedia.org/wiki/Trachtenberg_system


     



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