Divisibility Dreams
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Any number is divisible by any other number (except zero). But when you need to know if a number is exactly divisible (with no remainder) by another, the following rules can tell you without having to actually perform the division. This makes it a dream when your task is to factor a larger number into its smaller multipliers.

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Divisibility Dreams Reference Sheets (3 across)
Cut out and keep one of these with you until you memorize each rule.


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A number is exactly divisible by:    
2 If it is even (ends in 0, 2, 4, 6, 8) [976].    
3

If its SOD (Sum Of Digits) is divisible by 3 [546: 5+4+6 = 15].

   
4 If it is even and its last 2 digits = 00 [300] or are divisible by 4 [316].    
5 If it ends in 0 [230] or 5 [765].    
6 If it follows rules for both 2 and 3 [462: 4+6+2 = 12].    
7 If its 1st digit/s minus twice its last digit = 0 [147: 14 (27) = 14 14 = 0] or is divisible by 7 [91: 9 (21) = 9 2 = 7].
* To seek 7 is futile (first minus twice last).
   
8 If it is even and its last 3 digits = 000 [5000] or are divisible by 8 [3888] or twice the first two of the 3 digits plus the last is divisible by 8 [3152: (215) + 2 = 30 + 2 = 32]. * He ate(8) & was too full (twice first plus last).    
9 If its SOD (Sum Of Digits) is divisible by 9 [2754: 2+7+5+4 = 18].    
10 If it ends in 0 [6370].    
11

If SOD(odd) SOD(even) = 0  [572: (5+2) 7 = 7 7 = 0]
or is divisible by 11  [
2816: (2+1) (8+6) = 3 14 = -11].

   
12 If it follows rules for both 4 and 3 [924: 9+2+4 = 15].    
 

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