The '''greatest common divisor''' ('''GCD''', or '''GCF''' ('''greatest common factor''')) of two or more [[integer]]s is the largest integer that
The GCD is sometimes called the '''greatest common factor''' ('''GCF''').
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2 KB (288 words) - 21:40, 26 January 2021
...ter than Silvia's. This pattern continues. So if Bernardo chooses the 29th greatest number or below, he will have <math>55 + 54 + 53 + \cdots + 1</math> pairs
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5 KB (794 words) - 17:19, 10 November 2024
...r any two [[relatively prime]] [[positive integer]]s <math>m,n</math>, the greatest integer that cannot be written in the form <math>am + bn</math> for [[nonne
...leq (m-1)n-m=mn-m-n</imath>, which shows that <imath>mn-m-n</imath> is the greatest number in the form <imath>cn-m</imath>. Any number greater than this and co
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17 KB (2,829 words) - 00:05, 9 November 2025
...ually. If there are <math>2000</math> gold coins in the chest, what is the greatest number of gold coins Tony could take as his share? (Assume each gold coin i
...math>40</math> nickels, he computes <math>88</math> as his score. Find the greatest number of nickels he could have successfully tossed into the jar.
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71 KB (11,749 words) - 11:39, 20 November 2024
...o the set, the average value of the integers rises to <math>40</math>. The greatest integer in the original set <math>S</math> is <math>72</math> greater than
Let <math>x</math> be the greatest integer, <math>y</math> be the smallest, <math>z</math> be the sum of the n
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7 KB (1,130 words) - 22:39, 23 September 2025
...en <imath>0</imath> and <imath>1</imath>. What is the probability that the greatest of these three numbers is greater than <imath>2</imath> times each of the o
...en <imath>0</imath> and <imath>1</imath>. What is the probability that the greatest of these three numbers is greater than the sum of the other two numbers?
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9 KB (1,402 words) - 01:01, 12 November 2025
...eatest integer function, also known as the '''floor function''', gives the greatest integer less than or equal to its argument. The floor of <math>x</math> is
...+\left[\frac{n}{10!}\right]=1999</math>. Here <math>[x]</math> denotes the greatest integer less than or equal to <math>x</math>.
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3 KB (508 words) - 20:05, 26 February 2024
...e of the difference between the greatest element of <math>A</math> and the greatest element of <math>B</math> is <math>99</math>. Find <math>m.</math>
...e number of elements as set <math>B</math>, and the difference between the greatest terms of the two two sequences is <math>99</math> (forget about absolute va
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8 KB (1,431 words) - 16:50, 29 December 2024
...use answer choices from greatest to least since the question asks for the greatest value.
Therefore, <math>\boxed{\text{(D)}}</math> is the greatest.
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3 KB (457 words) - 01:16, 5 July 2021
Which of the following polynomials has the greatest real root?
...Clearly, <math>\boxed{\textbf{(B) } x^{17}+2018x^{11}+1}</math> has the greatest real root.
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14 KB (2,361 words) - 13:41, 20 August 2025
...e clockwise, as shown in part in the diagram below. What is the sum of the greatest number and the least number that appear in the second row from the top?
...r of interior pieces as pieces along the perimeter of the pan. What is the greatest possible number of brownies she can produce?
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17 KB (2,425 words) - 18:08, 9 November 2025
...here <math> a, b, </math> and <math> c </math> are positive integers whose greatest common divisor is 1. Find <math> a^2+b^2+c^2. </math>
...ath> n, </math> let <math> S_n=\sum_{k=1}^{2^{n-1}}g(2k). </math> Find the greatest integer <math> n </math> less than 1000 such that <math> S_n </math> is a p
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7 KB (1,173 words) - 02:31, 4 January 2023
...n=1,2,3,\ldots</math> For each <math>n</math>, let <math>d_n</math> be the greatest common divisor of <math>a_n</math> and <math>a_{n+1}</math>. Find the maxim
If <math>(x,y)</math> denotes the [[greatest common divisor]] of <math>x</math> and <math>y</math>, then we have <math>d
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5 KB (795 words) - 21:27, 19 December 2024
Let <math>N</math> be the greatest integer multiple of 8, no two of whose digits are the same. What is the rem
...igit to occupy the rightmost side. Therefore, the last three digits of the greatest number should be an arrangement of the digits <math>0,1,2</math>. Since the
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2 KB (315 words) - 10:35, 18 August 2024
...enerality, assume that the set <math>\{a\}</math> is ordered from least to greatest so that the bounding condition becomes <math>a_n \le n \cdot a_1.</math> No
...The smallest possible value for <math>c_{n+1}</math> is the sum of the two greatest values of <math>\{s_n\}</math> which are <math>F_{n-1}</math> and <math>F_n
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5 KB (943 words) - 20:26, 14 August 2025
...s <math>A</math> and <math>C</math> is <math>44</math> pounds. What is the greatest possible integer value for the mean in pounds of the rocks in the combined
Thus, the greatest integer value is <math>y=59</math>, choice <math>(E)</math>.
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8 KB (1,363 words) - 21:37, 13 October 2024
...penny and at least one nickel. What is the difference in cents between the greatest possible and least amounts of money that Ricardo can have?
...s the greatest number of pennies; as he must have at least one nickel, the greatest number of pennies he can have is also <math>2019</math>, giving him a total
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3 KB (430 words) - 23:50, 20 August 2025
...algorithm''' or '''Euclid's algorithm''') is an algorithm that finds the [[greatest common divisor]] (GCD) of two elements of a [[Euclidean domain]], the most
...> and <math>r</math>, it should divide <math>{a}</math> as well. Thus, the greatest common divisors of <math>{a}</math> and <math>b</math> and of <math>b</math
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6 KB (923 words) - 16:39, 30 September 2024
...ll those integers. For any [[set]] of [[positive integer]]s, there is a [[greatest common divisor]].
* Find the greatest common divisor of 12, 99, and 111.
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543 bytes (75 words) - 09:14, 14 October 2025
...the elements of <math>S</math>. Find the sum of all possible values of the greatest element of <math>S</math>.
...78,79\}</math> and <math>\{89,90,91,92.\}</math>. Therefore the sum of the greatest elements of the possible sets <math>S</math> is <math>37+50+79+92=\boxed{25
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16 KB (2,416 words) - 16:48, 20 January 2025
