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1): The prime factorization of 198 is  198 = 2 · 32 · 11 A): 2 · 3.3· 11 B): 2.33.3 C): 1.198 D): 18.11   2): Some numbers and their prime factorizations are given below. 140 = 22 5 · 7 175 = 52 7 532 = 22 7 · 19 648 = 23 34 1078 = 2 · 72 11 1083 = 3 · 192 15435 = 32 5 · 73 1078 = 2 · 72 11 25480 = 23 5 · 72·13 Using these prime factorizations the  gcd(532, 15435) = A): 7 B): 52 C): 97 D): 77   3): Applying the Euclidean Algorithm and the Extended Euclidean Algorithm.  the gcd(81,60) , and expression of the gcd as a linear combination of the two numbers =  A): gcd=3, combination = 3.81-4.60 B): gcd=3, combination = 21-18 C): gcd=12, combination = 81-69 D): gcd=9, combinaton = 81-60-12

1): The prime factorization of 198 is  198 = 2 · 32 · 11 A): 2 · 3.3· 11 B): 2.33.3 C): 1.198 D): 18.11   2): Some numbers and their prime factorizations are given below. 140 = 22 5 · 7 175 = 52 7 532 = 22 7 · 19 648 = 23 34 1078 = 2 · 72 11 1083 = 3 · 192 15435 = 32 5 · 73 1078 = 2 · 72 11 25480 = 23 5 · 72·13 Using these prime factorizations the  gcd(532, 15435) = A): 7 B): 52 C): 97 D): 77   3): Applying the Euclidean Algorithm and the Extended Euclidean Algorithm.  the gcd(81,60) , and expression of the gcd as a linear combination of the two numbers =  A): gcd=3, combination = 3.81-4.60 B): gcd=3, combination = 21-18 C): gcd=12, combination = 81-69 D): gcd=9, combinaton = 81-60-12

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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1): The prime factorization of 198 is 

198 = 2 · 32 · 11

A): 2 · 3.3· 11
B): 2.33.3
C): 1.198
D): 18.11
 

2): Some numbers and their prime factorizations are given below.

  • 140 = 22 5 · 7
  • 175 = 52 7
  • 532 = 22 7 · 19
  • 648 = 23 34
  • 1078 = 2 · 72 11
  • 1083 = 3 · 192
  • 15435 = 32 5 · 73
  • 1078 = 2 · 72 11
  • 25480 = 23 5 · 72·13

Using these prime factorizations the  gcd(532, 15435) =


A): 7
B): 52
C): 97
D): 77
 

3): Applying the Euclidean Algorithm and the Extended Euclidean Algorithm.

 the gcd(81,60) , and expression of the gcd as a linear combination of the two numbers = 


A): gcd=3, combination = 3.81-4.60
B): gcd=3, combination = 21-18
C): gcd=12, combination = 81-69
D): gcd=9, combinaton = 81-60-12
 
4): using arithmetic in the ring of integers mod 9,
5×8inZ9=

A): 4
B): 36
C): 2
D): 0
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