CAT Questions | CAT Number Systems Questions | Factors

A CAT Number systems question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Factors, Factorials, HCF and LCM, base system & remainders of the above mentioned concepts. In CAT Exam, one can generally expect to get 1 question from CAT Number Systems involving Factors.CAT Quantitiative Aptitude questions from Factors involve ideas like Sum of Factors, Odd factors, Even Factors and so on. CAT Number Systems is an important topic with lots of weightage in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

1. CAT Number Systems - Factors

   The sum of the factors of a number is 124. What is the number?
   
   A. Number lies between 40 and 50
   
   B. Number lies between 50 and 60
   
   C. Number lies between 60 and 80
   
   D. More than one such number exists
   
   

   Correct Answer

   Choice D
   More than one such number exists

   Explanation
   

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2. CAT Number Systems - Factors

   How many factors of 1080 are perfect squares?
   
   A. 4
   
   B. 6
   
   C. 8
   
   D. 5
   
   

   Correct Answer

   Choice A
   4

   Explanation
   

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3. CAT Number Systems - Factors

   How many factors of 2⁵ × 3⁶ × 5² are perfect squares?
   
   A. 18
   
   B. 24
   
   C. 36
   
   D. 8
   
   

   Correct Answer

   Choice B
   24

   Explanation
   

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4. CAT Number Systems - Odd Factors

   How many factors of 2⁴ × 5³ × 7⁴ are odd numbers?
   
   A. 12
   
   B. 8
   
   C. 15
   
   D. 30
   
   

   Correct Answer

   Choice C
   15

   Explanation
   

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5. CAT Number Systems - Factors

   How many factors of the number 2⁸ × 3⁶ × 5⁴ × 10⁵ are multiples of 120?
   
   A. 540
   
   B. 660
   
   C. 594
   
   D. 792
   
   

   Correct Answer

   Choice C
   594

   Explanation

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6. CAT Number Systems - Even Factors

   Number N = 2⁶ × 5⁵ × 7⁶ × 10⁷; how many factors of N are even numbers?
   
   A. 1183
   
   B. 1200
   
   C. 1050
   
   D. 840
   
   

   Correct Answer

   Choice A
   1183

   Explanation

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7. CAT Number Systems - Perfect Cube

   Numbers A, B, C and D have 16, 28, 30 and 27 factors. Which of these could be a perfect cube?
   
   A. A and B
   
   B. B and C
   
   C. A, B and C
   
   D. B and D
   
   

   Correct Answer

   Choice A
   A and B

   Explanation

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8. CAT Number Theory 'abcabc'

   If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?
   
   A. 16 factors
   
   B. 24 factors
   
   C. 16 or 24 factors
   
   D. 20 factors
   
   

   Correct Answer

   Choice C
   16 or 24 factors

   Explanation

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9. CAT Number Systems - Brute Force

   How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?
   
   A. 61
   
   B. 56
   
   C. 52
   
   D. 65
   
   

   Correct Answer

   Choice A
   61

   Explanation
   

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10. CAT Number Systems - 18 factors

    Find the smallest number that has exactly 18 factors.
    
    A. 180
    
    B. 216
    
    C. 240
    
    D. None of these
    
    

    Correct Answer

    Choice A
    180

    Explanation
    

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11. CAT Number Systems - Factors

    A number N² has 15 factors. How many factors can N have?
    
    A. 5 or 7 factors
    
    B. 6 or 8 factors
    
    C. 4 or 6 factors
    
    D. 9 or 8 factors
    
    

    Correct Answer

    Choice B
    6 or 8 factors

    Explanation
    

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12. CAT Number Theory 'abcabc'

    If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?
    
    A. 16
    
    B. 24
    
    C. 18
    
    D. 30
    
    

    Correct Answer

    Choice A
    16

    Explanation
    

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13. CAT Number Systems - 12 Factors

    What is the smallest number that has exactly 12 factors?
    
    A. 211
    
    B. 60
    
    C. 120
    
    D. 144
    
    

    Correct Answer

    Choice B
    60

    Explanation
    

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