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Generalized Divisibility Rule of Natural Number m

Journal: The Journal of the Institute of Internet, Broadcasting and Communication (Vol.14, No. 5)

Publication Date:

Authors : ;

Page : 87-93

Keywords : Divisibility test; Modular; Digits reduction; Most left digit; Most right digit;

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Abstract

For n/m - qm + r , there is no simple divisibility rule for simple m = 7 such that is the n multiply by m? This problem can be more complex for two or more digits of m. The Dunkels method has been known for generalized divisibility test method, but this method can not compute very large digits number that can not processed by computer. This paper suggests simple and exact divisibility method for m completely irrelevant n and m of digits. The proposed method sets  r1 = n1n2 ? n1(mod m) for n = n1n2n3 ? nk, m = m1m2 ? m1m2. Then this method computes  r1 = r1 = 1 × 10 + n1(mod m), i = 2, 3, ?, k-1+1 and reduces the digits of n one-by-one. The proposed method can be get the quotient and remainder with easy, fast and correct for various n, m experimental data.

Last modified: 2016-01-19 13:39:45