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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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