Divisibility Tests

Lyon and Tiger were on a roll this morning. This was their effort and they wanted a record kept on our blog. The research was theirs; I only helped with the edits. If anyone out there finds the contents of the table useful, brilliant.

DIVISIBLE BY: TEST EXAMPLE
2 If the last digit is an even number 1002 or 19904 or 345402
3 If the sum of the digits is divisible by 3 540 or 207
4 If the last two digits are divisible by 4 1040 or 99948
5 If the last digit is 0 or 5 1000 or 99905
6 If the number is divisible by both 2 AND 3 1002 or 2136
7 If 7 is a factor of the number 7 or 42 or 63
8 If the last 3 numbers are divisible by 8 10106 or 99839080
9 If the sum of the digits is divisible by 9 1008 or 9000
10 If the last digit is 0 1730 or 3330
11 If the difference between the sum of all alternate digits is zero or 11 for example, the number 1320, 1 + 2 = 3; 3 + 0 = 3. The difference between the two sums is zero so the number is divisible by 11. Another way of doing this is placing + and – before alternate digits to check if the result is zero or 11 so using 1320 again,  +1-3+2-0 = 0 so 1320 is divisible by 11. 1320 or 1419
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