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Divisibility

You can divide 6 into equal parts of 1, 2, 3, or 6 (but not 4 or 5) because 6 is divisible by these numbers. The rules of divisibility have wide-ranging applications as an easy test for divisibility.

Deriving Divisibility Rules

         

What is true of all numbers that are divisible by 3?

Which of the following is true for all integers that are divisible by \(18?\)

\[ \begin{align} A :& \text{The last digit is even.} \\ B :& \text{The last digit is 0 or 5.}\\ C :& \text{The sum of their digits is a multiple of 7.} \\ D :& \text{The sum of their digits is a multiple of 9.} \end{align}\]

Which of the following integers is divisible by 8?

An integer is divisible by 11 if and only if:

If we know that an integer is a multiple of 2, how many possibilities are there for its units digit (last digit)?

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