Ll CSET 110 - Number Theory Mc

15 Questions | Total Attempts: 61

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Ll CSET 110 - Number Theory Mc

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

  • 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

  • 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

  • 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. 
  • 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

  • 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

  • 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

  • 8. 
    The greatest common divisor of . How many factors of X are there?
    • A. 

      12

    • B. 

      16

    • C. 

      24

    • D. 

      36

  • 9. 
    What is the greatest common divisor of 4986, 5022, 5058, and 5490?
    • A. 

      6

    • B. 

      9

    • C. 

      12

    • D. 

      18

  • 10. 
    Find the least common multiple of 12, 18, 24, and 30.
    • A. 

      240

    • B. 

      360

    • C. 

      720

    • D. 

      2160

  • 11. 
    Find the least common multiple of 18, 27, 36, 48, 81.
    • A. 

      1260

    • B. 

      1440

    • C. 

      1620

    • D. 

      4860

  • 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

  • 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

  • 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. 
  • 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

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