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" Measure, of two or more quantities, is the greatest quantity that will exactly divide each of them. "
New University Algebra: A Theoretical and Practical Treatise, Containing ... - Page 52
by Horatio Nelson Robinson - 1863 - 420 pages
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...proper fraction'. § II. Method of finding the Greatest Common Divisor of two or more Quantities. 130. The greatest common divisor of two or more quantities, is the greatest quantity which divides each of them exactly. Thus, the greatest common divisor of the quantities 16«363, 12«36<*...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...proper frac* tion. § IF. Method of finding the Greatest Common Divisor of two or more Quantities. 130. The greatest common divisor of two or more quantities, is the greatest quantity which divides each of them exactly. Thus, the greatest common divisor of the quantities 16a2i°, 12a24o...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...divided ly their sum. 30 SECTION XV. GREATEST COMMON DIVISOR.— PERMUTATIONS AND COMBINATIONS. (249.) THE greatest common divisor of two or more quantities is the greatest factor which is common to each of the quantities. tPROPOSITION. The greatest common divisor of two...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...divided by their sum. 30 SECTION XV. GREATEST COMMON DIVISOR.— PERMUTATIONS AND COMBINATIONS. (249.) THE greatest common divisor of two or more quantities is the greatest factor which is common to each of the quantities. • PROPOSITION. The greatest common divisor of two...
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...SECTION XV. GREATEST COMMON DIVISOR.— CONTINUED FRACTIONS.— PERMUTATIONS AND COMBINATIONS. (249.) The greatest common divisor of two or more quantities is the greatest factor which is common to each of the quantities. THEOREM. The greatest common divisor of two quantities...
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The University Algebra ...

John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...quantities is one that is exactly contained in each of them. (129.) The greatest common measure or greatest common divisor of two or more quantities is the greatest quantity that is exactly contained in each of them. • THEOREM I. (13U.) If a quantity measures another quantity...
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New Elementary Algebra: in which the First Principles of Analysis are ...

Benjamin Greenleaf - 1863 - 338 pages
...remainder. Hence, any factor common to two or more quantities is a common divisor of those quantities. 96, The GREATEST COMMON DIVISOR of two or more quantities is the greatest quantity that will divide each of them without a remainder. Hence, the greatest common divisor of two or more quantities...
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...— 6=x, 6 — c=y, and c — a=z, prove that 2(o — b*)'(b — c)' +2(a— 6)'(c— a)'+2C6— c)'( THE GREATEST COMMON DIVISOR 97. A Common Divisor of...algebraic or its arithmetical value. Thus, if x — 3 and a;"-(-4x-)-2 are the prime factors common to two or more quantities, then according to the above definition,...
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New Higher Algebra: An Analytical Course Designed for High Schools ...

Benjamin Greenleaf - Algebra - 1864 - 420 pages
...Also, when quantities are prime to each other, they have no common measure greater than unity. 104. The GREATEST COMMON DIVISOR of two or more quantities is the greatest quantity that will divide each of them without a remainder. By the greatest of two or more algebraic quantities, it may...
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Algebra: Adapted to the Course of Instruction Usually Pursued in the ...

Paul Allen Towne - Algebra - 1865 - 314 pages
...4). 12. Factor 7a^— 7x — 84, 5*3- 5a; — 60 and x3 — 13x2 + 42a; GREATEST COMMON DIVISOR. 81. The Greatest Common Divisor of two or more quantities is the greatest quantity that will divide each of them without a remainder. Thus, xy is the greatest common divisor of x3y and xy'. 82....
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