| Divisor |
Articles about Divisor |
Information AboutDivisor |
| CATEGORIES ABOUT DIVISOR | |
| elementary number theory | |
| elementary arithmetic | |
| SHOPPER'S DELIGHT | |
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In Mathematics , a divisor of an Integer ''n'', also called a '''factor''' of ''n'', is an integer which evenly divides ''n'' without leaving a Remainder . EXPLANATION | ||
| In General, We Say ''m''''n'' (read: ''m'' Divides ''n'') For Non-zero Integers ''m'' And Integers ''n'' | "http://wwwinformationdelightinfo/encyclopedia/entry/Vrhbosna/iff" class="copylinks">Iff there exists an integer ''k'' such that ''n'' = ''km'' Thus, divisors can be Negative as well as positive 1 and &minus1 are divisors of every integer, every integer is a divisor of itself, and every integer is a divisor of 0, except by convention 0 itself (see also Division By Zero ) Numbers divisible by 2 are called Even and those that are not are called Odd |
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| If ''a'' ''b'' And ''b'' ''c'', Then ''a'' ''c'' ( | "http://wwwinformationdelightinfo/encyclopedia/entry/Vrhbosna/transitive_relation" class="copylinks">Transitive Relation ) |
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| If ''a'' ''b'' And ''b'' ''a'', Then ''a'' | ''b'' or ''a'' = &minus''b'' |
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| If ''a'' ''bc'', And | "http://wwwinformationdelightinfo/encyclopedia/entry/Vrhbosna/greatest_common_divisor" class="copylinks">Gcd (''a'',''b'') = 1, then ''a'' ''c'' ( Euclid's Lemma ) |
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| The Relation Of Divisibility Turns The Set '''N''' Of | "http://wwwinformationdelightinfo/encyclopedia/entry/Vrhbosna/negative_and_non-negative_numbers" class="copylinks">Non-negative integers into a Partially Ordered Set , in fact into a Complete Distributive Lattice The largest element of this lattice is 0 and the smallest one is 1 The meet operation ^ is given by the Greatest Common Divisor and the join operation v by the Least Common Multiple This lattice is isomorphic to the dual of the lattice of Subgroup s of the infinite Cyclic Group '''Z''' |
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| We Can Generalize This Method Even Further To Find How To Check Divisibility Of Any Integer In Any Base By Any Other (smaller Integer) Let Us Say That We Want To Determine If ''d'' ''a'' In | "http://wwwinformationdelightinfo/encyclopedia/entry/Vrhbosna/numeral_system" class="copylinks">Base ''b'' Then we first find a pair of integers (''n'', ''k'') that solves the congruence ''b''<sup>''n''</sup> &equiv ''k'' ( Mod ''d'') Now rather than summing the digits, we take ''a'' (which has ''m'' digits) and multiply the first ''m''-''n'' digits by ''k'' and add the product to the last (or more precisely, smallest) ''k'' digits and repeat if necessary If the result is a multiple of ''d'' then the original number is divisible by ''d'' |