Number Theory


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

For how many different values of AA is 27A427A4 (a four digit number where the third digit is AA) divisible by 6?

For how many different values of AA is the three digit number 3A63A6 even?

Note: AA can be any of the 10 digits from 0 to 9.


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