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Divisibility

You can divide 6 into equal parts of 1, 2, 3, or 6 (but not 4 or 5) because 6 is divisible by these numbers. The rules of divisibility have wide-ranging applications as an easy test for divisibility.

Level 2

         

Is 87985 divisible by 7?

Find the smallest positive multiple of nine containing only even digits.

How many perfect squares have the property that all of their digits are equal?

Details and Assumptions

  • For this question, \(0=0^2 \) is also a perfect square.

Given that \(a\) and \(b\) are integers, what can we conclude about the expression

\[ \left( { a }^{ 2 }+a+2011 \right) \left( 2b+1 \right) ? \]

\[\frac{(n+2)!}{(n-1)!}\] The above fraction is divisible by which of the following?

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