Quick verify multiplication

Math Online Tom Circle

Verify:2,578,314  x 6,321,737 = 16,299,423,011,418 ?

2,578,314  => (2+5+7+8+3+1+4)) =30 => (3+0) = 3

6,321,737 => (6+3+2+1+7+3+7)=29 => 2+9 = 11 => (1+1) = 2

3 x 2 = 6 

16,299,423,011,418 => (1+6+2+9+9+4+2+3+0+1+1+4+1+8) = 51 => (5+1) = 6

Correct !

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2 Responses to Quick verify multiplication

  1. boredstudent says:

    Hi could you explain how this works?

    Like

  2. Thanks for your interest.
    The method above is called the Digit Sum method, here is a really nice website explaining it (http://mikespivey.wordpress.com/2011/12/27/digit-sums/)
    The key theorem is that the Digit sum is actually the remainder of the number when divided by 9.
    For example, for the number 82, 8+2=10, 1+0=1, and 82 divided by 9 gives remainder 1.

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