Number Theory

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Remainder Theorem

Some important points to find remainder

  1. \(\left[ {\mathop {nnnn.......nnnn}\limits_{(p - 1)\,times} } \right]\) is always divisible by \(p\), where \(p\) is a prime number more than 5.
  2. Any number formed by repeating a digit 4 times is always multiple of 11 and  101
  3. Any number formed by repeating a digit 5 times is always multiple of 41 and  271
  4. Any number formed by repeating a digit 6 times is always multiple of 3, 7, 11, 13, 37 
  5. Divisibility of a number formed by repeating a digit n time can be established by using various divisibility theorems.

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