SOLUTION: Your class has just completed a unit on divisibility rules. One of the students asks why divisibility by numbers other than 3 and 9 can not be tested by dividing the sum of the di

Question 174141: Your class has just completed a unit on divisibility rules. One of the students asks why divisibility by numbers other than 3 and 9 can not be tested by dividing the sum of the digits by the tested number. How do you respond?
Answer by rajagopalan(174) (Show Source): You can put this solution on YOUR website!
why divisibility by numbers other than 3 and 9 can not be tested by dividing the sum of the digits by the tested number.
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Basis: All multiples of 3 (3, 6, 9, 12, 15, 18..etc) have digits which sum up to 3, 6, 9 only in a cyclic fashion. Hence these two digits are amenable to the law of "Sum and divide".
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Other numbers divsible by digits..2, 4, 5, 7 and 8 sum up to odd numbers also ( eg 12 divisible by 2 and 4 sums to 3 an odd number, 16 divisible by 8 sums to 7 an odd number).
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Hence the 3,6,9 Rule is not extendable to other digits for divisibility test.
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