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### DIVISIBILITY OF INTEGERS

• 2 is a factor of all even numbers.
• 3 is a factor when the sum of the digits is divisible by 3.
• 4 is a factor when the rightmost two digits are a 0 or a number divisible by 4.
• 5 is a factor when the units digit is 5 or 0.
• 6 is a factor of all even numbers that are divisible by 3.
• 7 is a factor if, writing the number as 10a + b, we find a - 2b is 0 or a multiple of 7.
• 8 is a factor when the rightmost three digits are zeros or a number divisible by 8.
• 9 is a factor when the sum of the digits is divisible by 9.
• 10 is a factor if the units digit is 0.
• 11 is a factor when the sum of the digits in the even places equals the sum of the digits in the odd places, or when the difference between these two sums is 11 or some multiple of 11.

Source: Arithmetic Refresher for Practical Men by A.A. Klaf.

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