Divisibility rules were used by almost everyone before calculators were invented. They are useful today because using them can save you a lot of time.
A number is divisible by the number if:  
2 
the last digit of the number is even: 0, 2, 4, 6, or 8

3 
the sum of the digits is divisible by 3 (with no remainder)

4 
the last two digits in the number is divisible by 4 (with no remainder)

5 
the last digit of the number is 0 or 5

6 
it is divisible by both 2 and 3 – use the rules above for 2 and 3

8 
if the last three digits are divisible by 8 (with no remainder)

9 
the sum of the digits is divisible by 9
1233 is divisible by 9 because 1 + 2 + 3 + 3 = 9 
10 
if the number ends in 0 
11 
if the sums of the alternate digits are different by 0, 11, 22, or 33, or any
twodigit multiple of 11. In other words, say you have a sixdigit number: Add up the first, third, fifth digits – the odd ones. Then add the digits in the even places – second, fourth, sixth. Then subtract those totals from each other, and if the answer is a multiple of 11, the original number is divisible by 11.

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Mrs. Shearer
Last Updated: 11/24/2005
© K. A. Shearer 20052009
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