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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 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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