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Number Theory

Divisibility

Divisibility Tests Warmup

         

Is 12345 divisible by 5?

Note: 12345 is divisible by 5 if it can be divided into groups of 5 with nothing left over.

Is 234 divisible By 9?

A number that consists entirely of 1s (like 1, 11, 111, etc.) is called a repunit. How many digits long is the smallest repunit that is divisible by 9?

For how many different values of \(A\) is \(27A4\) (a four digit number where the third digit is \(A\)) divisible by 6?

For how many different values of \(A\) is the three digit number \(3A6\) even?

Note: \(A\) can be any of the 10 digits from 0 to 9.

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