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Number Theory


Application of Divisibility Rules


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

How many digits \(N\) are there such that the six-digit integer \(\overline{1 2 3 3 N 2} \) is a multiple of 8?

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

How many three-digit numbers are not divisible by \( 5, \) have digits that sum to \( 15, \) and have the first digit equal to the third digit?

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


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