Understanding Factors: A Complete Guide

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A. Find the Factors (1–20)

Find all factors of the given numbers.

  1. Factors of 12
  2. Factors of 18
  3. Factors of 20
  4. Factors of 24
  5. Factors of 27
  6. Factors of 30
  7. Factors of 32
  8. Factors of 36
  9. Factors of 40
  10. Factors of 42
  11. Factors of 45
  12. Factors of 48
  13. Factors of 50
  14. Factors of 54
  15. Factors of 56
  16. Factors of 60
  17. Factors of 63
  18. Factors of 72
  19. Factors of 80
  20. Factors of 90

B. Multiple-Choice (21–35)

Choose the correct answer.

  1. Which of these is not a factor of 36?
    a) 3 b) 4 c) 5 d) 12
  2. Which number has exactly 2 factors?
    a) 11 b) 15 c) 21 d) 25
  3. Which of the following is a factor of 72?
    a) 7 b) 8 c) 6 d) Both b and c
  4. What is the greatest factor of any number?
    a) 0 b) 1 c) The number itself
  5. Which number is a common factor of 12 and 18?
    a) 2 b) 3 c) 6 d) All of these
  6. Which of these numbers is not a factor of 50?
    a) 2 b) 5 c) 10 d) 15
  7. The number 1 is a factor of:
    a) only even numbers b) only odd numbers c) all numbers
  8. Which number has more factors?
    a) 24 b) 23
  9. Which of the following is a factor of 96?
    a) 12 b) 11 c) 7
  10. Which of the following is a factor of 81?
    a) 9 b) 10 c) 12
  11. Which is a factor of 64?
    a) 6 b) 8 c) 3
  12. 14 is a factor of which number?
    a) 40 b) 56 c) 70
  13. Which number has 3 as a factor?
    a) 22 b) 25 c) 27
  14. Which pair shows common factors of 15 and 20?
    a) 1 and 5 b) 3 and 5 c) 5 and 15
  15. Which number has the fewest factors?
    a) 13 b) 14 c) 16

C. Word / Concept Problems (36–50)

  1. Write any two factors of 28.
  2. Write the smallest factor of 36.
  3. Write the greatest factor of 54.
  4. List the first four multiples of 9 (to understand factors vs multiples).
  5. Find two common factors of 24 and 40.
  6. Name a prime number between 20 and 30.
  7. Name a composite number between 10 and 20.
  8. Which number has more factors: 18 or 19?
  9. Write a number that is a factor of both 32 and 48.
  10. Write the even factors of 16.
  11. How many total factors does 12 have?
  12. Write any three factors of 35.
  13. Is 9 a factor of 90? (Yes/No)
  14. Write the common factors of 10 and 25.
  15. Which number has exactly 3 factors?
    Hint: Perfect squares of primes.

📘 ANSWER KEY

A. Find the Factors

  1. 1, 2, 3, 4, 6, 12
  2. 1, 2, 3, 6, 9, 18
  3. 1, 2, 4, 5, 10, 20
  4. 1, 2, 3, 4, 6, 8, 12, 24
  5. 1, 3, 9, 27
  6. 1, 2, 3, 5, 6, 10, 15, 30
  7. 1, 2, 4, 8, 16, 32
  8. 1, 2, 3, 4, 6, 9, 12, 18, 36
  9. 1, 2, 4, 5, 8, 10, 20, 40
  10. 1, 2, 3, 6, 7, 14, 21, 42
  11. 1, 3, 5, 9, 15, 45
  12. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  13. 1, 2, 5, 10, 25, 50
  14. 1, 2, 3, 6, 9, 18, 27, 54
  15. 1, 2, 4, 7, 8, 14, 28, 56
  16. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  17. 1, 3, 7, 9, 21, 63
  18. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
  19. 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
  20. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

B. Multiple-Choice

  1. c
  2. a
  3. d
  4. c
  5. d
  6. d
  7. c
  8. a
  9. a
  10. a
  11. b
  12. b
  13. c
  14. a
  15. a

C. Word / Concept Problems

  1. (Any 2) 1, 2, 4, 7, 14, 28
  2. 1
  3. 54
  4. 9, 18, 27, 36
  5. 1, 2, 4, 8 (any two)
  6. 23 or 29
  7. 12, 14, 15, 16, 18 (any one)
  8. 18
  9. 16 (or 1, 2, 4, 8)
  10. 2, 4, 8, 16
  11. 6
  12. 1, 5, 7, 35 (any three)
  13. Yes
  14. 1, 5
  15. 4 (factors: 1, 2, 4) or 9 (1, 3, 9) or 25 (1, 5, 25)
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