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.

Find the digit \(N\) such that the three digit integer \( \overline{ 5 7 N} \) is a multiple of 9.

Find the digit \(N\) such that the five-digit number \(\overline{N878N}\) is divisible by 9.

How many 5 digit positive integers are multiples of 11, and have digits which sum to 43?

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