Ll CSET 110 - Number Theory Mc

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| By Justin Gillette
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Justin Gillette
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Quizzes Created: 2 | Total Attempts: 328
Questions: 15 | Attempts: 143

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Ll CSET 110 - Number Theory Mc - Quiz

Questions and Answers
  • 1. 

    5,078 = 150(33)+128 is the first step in finding the greatest common divisor of two numbers. Which of the following is the next step in the Euclidian Algorithm?

    • A.

      150=33(4)+18

    • B.

      128=33(3)+29

    • C.

      150=128(1)+22

    • D.

      5,078=128(39)+86

    Correct Answer
    C. 150=128(1)+22
  • 2. 

    The Euclidian Algorithm is performed to find the greatest common divisor of 1,622 and 136. Which of the following is a step in this Euclidian Algorithm?

    • A.

      136 = 11(12)+4

    • B.

      126=15(8)+6

    • C.

      126=12(10)+6

    • D.

      64=8(8)+0

    Correct Answer
    C. 126=12(10)+6
  • 3. 

    If  can be simplified to a fraction form , where a and b are mutually prime integers, what is a+b?

    • A.

      76

    • B.

      81

    • C.

      100

    • D.

      300

    Correct Answer
    C. 100
  • 4. 

    If a and b share a greatest common divisor of c, what is the least common multiple of a and b?

    • A.

      Abc

    • B.

      Ab

    • C.
    • D.
    Correct Answer
    C.
  • 5. 

    If  can be simplified to a fraction form , where a and b are mutually prime integers, what is a+b?

    • A.

      98

    • B.

      109

    • C.

      126

    • D.

      327

    Correct Answer
    B. 109
  • 6. 

    Let P represent the set of all numbers of the form  where x, y, and z are prime numbers less than 20. How many elements are contained in set P ?

    • A.

      56

    • B.

      512

    • C.

      729

    • D.

      6561

    Correct Answer
    B. 512
  • 7. 

    How many factors does  have if x, y, and z are integers?

    • A.

      Xyz

    • B.

      X+y+z

    • C.

      (x+1)(y+1)(z+1)

    • D.

      105

    Correct Answer
    C. (x+1)(y+1)(z+1)
  • 8. 

    The greatest common divisor of . How many factors of X are there?

    • A.

      12

    • B.

      16

    • C.

      24

    • D.

      36

    Correct Answer
    A. 12
  • 9. 

    What is the greatest common divisor of 4986, 5022, 5058, and 5490?

    • A.

      6

    • B.

      9

    • C.

      12

    • D.

      18

    Correct Answer
    D. 18
  • 10. 

    Find the least common multiple of 12, 18, 24, and 30.

    • A.

      240

    • B.

      360

    • C.

      720

    • D.

      2160

    Correct Answer
    B. 360
  • 11. 

    Find the least common multiple of 18, 27, 36, 48, 81.

    • A.

      1260

    • B.

      1440

    • C.

      1620

    • D.

      4860

    Correct Answer
    C. 1620
  • 12. 

    How many integers between 1 and 1000, inclusive, are a multiple of either 3 or 7?

    • A.

      381

    • B.

      428

    • C.

      430

    • D.

      475

    Correct Answer
    B. 428
    Explanation
    Err...Answer really IS 428. 333+142-47=428. Yay, mental arithmetic!

    Rate this question:

  • 13. 

    How many integers between 1 and 1000, inclusive, are a multiple of either 5 or 9?

    • A.

      288

    • B.

      289

    • C.

      311

    • D.

      312

    Correct Answer
    B. 289
  • 14. 

    To prove that  , the first step in a proof by mathematical induction is which of the following?

    • A.

       is also true.

    • B.
    • C.
    • D.
    Correct Answer
    C.
  • 15. 

     has a positive integer exponents and  is between 4000 and 5000, which of the following could be x+y+z?

    • A.

      6

    • B.

      9

    • C.

      11

    • D.

      15

    Correct Answer
    B. 9

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  • Current Version
  • Aug 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Apr 08, 2014
    Quiz Created by
    Justin Gillette
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