To see if a number can be evenly divided by:

2-  It must be even (ending in 0, 2, 4, 6, or 8).

3-  Add the digits and divide the sum by 3.

Examples:  234, 2+3+4=9, yes, 234 is divisible by 3

101, 1+0+1=2 no, 101 is not divisible by 3

4-  Take the last 2 digits, but don’t add them.  If the number formed by the last 2 digits is divisible by 4, then the whole number is.  All numbers divisible by 4 will also be even.

Examples:  1134, 34/4?  No, 1134 is not divisible by 4

1128, 28/4?  Yes, 1128 is divisible by 4

5-  The number must end in 0 or 5

6-  The number must be divisible by 2 and 3

7-  no short cut, just try dividing by 7 and see if it works

8-  no short cut, just try dividing by 8 and see if it works

9-  (Similar to the rule for 3)  Add the digits and divide the sum by 9. 

Examples:  981, 9+8+1=18, 18/9?, yes, 981 is divisible by 9

111, 1+1+1=3, 3/9?, no 111 is not divisible by 9

10-  It must end with a 0.

25- The last 2 digits must be 00, 25, 50, or 75

100-  It must end with 00

If you know a number is not prime, but you haven’t found a factor from 2 to 15, try dividing by prime numbers:  17, 19, 23, 29, 31, 37…

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