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Number Theory - Divisibility Rules

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Rule for divisibility by 10

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A number is divisible by 10 if its last digit is 0.

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Rule for divisibility by 3

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A number is divisible by 3 if the sum of its digits is divisible by 3.

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Rule for divisibility by 5

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A number is divisible by 5 if its last digit is 0 or 5.

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Rule for divisibility by 9

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A number is divisible by 9 if the sum of its digits is divisible by 9.

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Rule for divisibility by 2

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A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

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Rule for divisibility by 8

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A number is divisible by 8 if the last three digits form a number that is divisible by 8.

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Rule for divisibility by 6

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A number is divisible by 6 if it is divisible by both 2 and 3.

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Rule for divisibility by 7

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To check divisibility by 7, take the last digit, double it, and subtract it from the rest of the number; if the result is divisible by 7 (including 0), so is the original number.

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Rule for divisibility by 11

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A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.

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Rule for divisibility by 4

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A number is divisible by 4 if the last two digits form a number that is divisible by 4.

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