CAT Practice : Number System: Factors

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The following topics are covered in the CAT quant section from Number system - HCF, LCM. Detailed explanatory answers, solution videos and slide decks are also provided.
  1. Number Theory - Factors

    The sum of the factors of a number is 124. What is the number?

    1. Number lies between 40 and 50
    2. Number lies between 50 and 60
    3. Number lies between 60 and 80
    4. More than one such number exists
    • Correct AnswerChoice (D).
      More than one such number exists.
      Correct answer
    • Explanatory Answer
    • Sum of factors
    • Hard
  2. Number Theory - Factors

    How many factors of 1080 are perfect squares?

    1. 4
    2. 6
    3. 8
    4. 5
    • Correct AnswerChoice (A).
      4
      Correct answer
    • Explanatory Answer
    • Factors - Perfect Squares
    • Medium
  3. Number Theory - Factors

    How many factors of 25 * 36 * 52 are perfect squares?

    1. 18
    2. 24
    3. 36
    4. 8
    • Correct AnswerChoice (B).
      24
      Correct answer
    • Explanatory Answer
    • Factors - Perfect Squares
    • Medium
  4. Number Theory - Odd Factors

    How many factors of 24 * 53 * 74 are odd numbers?

    1. 100
    2. 99
    3. 20
    4. 24
  5. Number Systems - Factors

    How many factors of the number 28 * 36 * 54 * 105 are multiples of 120?

    1. 540
    2. 660
    3. 594
    4. 792
  6. Number Theory - Even Factors

    Number N = 26 * 55 * 76 * 107; how many factors of N are even numbers?

    1. 1183
    2. 1200
    3. 1050
    4. 840
    • Correct AnswerChoice (A).
      1183
      Correct answer
    • Explanatory Answer
    • Factors - Even numbers
    • Medium
  7. Number Theory - Perfect Cube

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

    1. A and B
    2. B and C
    3. A, B and C
    4. B and D
    • Correct AnswerChoice (A).
      A and B
      Correct answer
    • Explanatory Answer
    • Factors of perfect cube
    • Medium
  8. Number Theory 'abcabc'

    If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?

    1. 16 factors
    2. 24 factors
    3. 16 or 24 factors
    4. 20 factors
    • Correct AnswerChoice (C).
      16 or 24 factors
      Correct answer
    • Explanatory Answer
    • Factors of a number abcabc
    • Hard
  9. Number Theory - Brute Force

    How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?

    1. 61
    2. 56
    3. 52
    4. 65
  10. Number Theory - 18 factors

    Find the smallest number that has exactly 18 factors.

    1. 180
    2. 216
    3. 240
    4. None of these
    • Correct AnswerChoice (A).
      180
      Correct answer
    • Explanatory Answer
    • Smallest number with 18 factors
    • Hard
  11. Number Theory - Factors

    A number N2 has 15 factors. How many factors can N have?

    1. 5 or 7 factors
    2. 6 or 8 factors
    3. 4 or 6 factors
    4. 9 or 8 factors
    • Correct AnswerChoice (B).
      6 or 8 factors
      Correct answer
    • Explanatory Answer
    • Number Theory - Factors
    • Medium
  12. 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?

    1. 16
    2. 24
    3. 18
    4. 30
    • Correct AnswerChoice (A).
      16
      Correct answer
    • Explanatory Answer
    • Factors of a number abcabc
    • Hard
  13. 12 Factors

    What is the smallest number that has exactly 12 factors ?

    1. 211
    2. 60
    3. 120
    4. 144

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