DIVISIBILITY RULES
A number is divisible by 2,
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if the number is even.
Examples:
Numbers like 542, 896 and 458 are divisible by 2 since they are even numbers.
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A number is divisible by 3,
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if the sum of the digits is divisible by 3
Examples:
456 is divisible by 3 because 4+5+6=15, and 15 is divisible by 3
849 is also divisible by 3 since the sum of its digits is divisible by 3 ( 8+4+9=21). 21÷3 = 7
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A number is divisible by 4,
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if the last two digits is divisible by 4.
Examples:
8920 is divisible by 4 since the its last two digits (20) is divisible by 4.
6344 is divisible by 4 because the last two digits 44 is divisible by 4. 44÷4 is 11
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A number is divisible by 5,
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if the last digit is 0 or 5
Examples: 820, 895, 485 and the like
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A number is divisible by 6,
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if the number is divisible by 2 and 3. It means that a number should be even and the sum of all digits is divisible by 3.
Example:
(see rule for 3 and 2 above)
456 is divisible by 3 because 4+5+6=15, and 15 is divisible by 3 at the same time it is even number. Thus, it is divisible by 6
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A number is divisible by 7
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if the difference between twice the last digit and the remaining digit form a number that is divisible by 7.
Example: 399
39-(9x2)=21, 21÷7=3
Since the result is divisible by 7, it means that 399 is divisible by 7
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A number is divisible by 8
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if the last three digits is divisible by 8
Examples:
Numbers like 854 048 and 1 652 208 are divisible by 8, since both last 3 digits of these numbers are divisible by 8. (048 or 48÷8 = 6, 208÷8 = 26)
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A number is divisible by 9
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if the sum of all digits is divisible by 9
Examples:
801 is divisible by 9 because 8+0+1 = 9, and 9 is divisible by itself. Likewise, 2286 is divisible by 9 since 2+2+8+6=18, and 18 is divisible by 9.
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A number is divisible by 10
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if the number ends with zero (0)
Examples: 560, 890, 12580 and the like are divisible by 10.
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A number is divisible by 11
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if the sum of the odd digits minus the sum of even digits is divisible by 11
Examples:
985 006 is divisible by 11 because
(9+5+0)-(8+0+6)=0 and 0 is divisible by 11. (0÷11=0)
7194 is also divisible by 11 since (7+9)-(1+4)=11, and the result (11) is divisible by 11.
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A number is divisible by 12
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if it is divisible by both 3 and 4
Example:
(see divisibility rule for 3 and 4 above)
780 is divisible by 12 since 7+8+0=15. The resulting sum of the digits (15) is divisible by 3. Thus, the number is divisible by 3. Moreover, the number is also divisible by 4 because the last two digits (80) is divisible by 4
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