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Fundamental theorem of arithmetic and Greatest common divisor

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Fundamental theorem of arithmetic and Greatest common divisor

Fundamental theorem of arithmetic vs. Greatest common divisor

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors. In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

Similarities between Fundamental theorem of arithmetic and Greatest common divisor

Fundamental theorem of arithmetic and Greatest common divisor have 17 things in common (in Unionpedia): D. C. Heath and Company, Ernst Kummer, Euclidean domain, Fermat's Last Theorem, Field (mathematics), Gaussian integer, Ideal (ring theory), Integer, Integer factorization, Least common multiple, Multiplicative function, Natural number, Prentice Hall, Principal ideal domain, Rational number, Unique factorization domain, Wolfram Demonstrations Project.

D. C. Heath and Company

D.C. Heath and Company was an American publishing company located at 125 Spring Street in Lexington, Massachusetts, specializing in textbooks.

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Ernst Kummer

Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician.

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Euclidean domain

In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of the integers.

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Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

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Ideal (ring theory)

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.

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Least common multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.

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Multiplicative function

In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1).

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Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

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Prentice Hall

Prentice Hall is a major educational publisher owned by Pearson plc.

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Principal ideal domain

In abstract algebra, a principal ideal domain, or PID, is an integral domain in which every ideal is principal, i.e., can be generated by a single element.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Unique factorization domain

In mathematics, a unique factorization domain (UFD) is an integral domain (a non-zero commutative ring in which the product of non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units, analogous to the fundamental theorem of arithmetic for the integers.

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Wolfram Demonstrations Project

The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.

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The list above answers the following questions

Fundamental theorem of arithmetic and Greatest common divisor Comparison

Fundamental theorem of arithmetic has 59 relations, while Greatest common divisor has 86. As they have in common 17, the Jaccard index is 11.72% = 17 / (59 + 86).

References

This article shows the relationship between Fundamental theorem of arithmetic and Greatest common divisor. To access each article from which the information was extracted, please visit:

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