Number Theory


Application of Divisibility Rules


Find the digit NN such that the three digit integer 57N \overline{ 5 7 N} is a multiple of 9.

How many digits NN are there such that the six-digit integer 1233N2\overline{1 2 3 3 N 2} is a multiple of 8?

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

How many three-digit numbers are not divisible by 5, 5, have digits that sum to 15, 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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