LL CSET 110 - Number Theory MC | Attempts: 143

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| By Justin Gillette

Justin Gillette

Community Contributor

Quizzes Created: 2 | Total Attempts: 330

Questions: 15 | Attempts: 143 | Updated: Dec 6, 2024

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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.

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

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.

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

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!

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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
Dec 06, 2024

Quiz Edited by
ProProfs Editorial Team
Apr 08, 2014

Quiz Created by
Justin Gillette

Ll CSET 110 - Number Theory Mc

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?

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?

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

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

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

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 ?

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

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

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

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

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

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

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

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

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