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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 41 · 40 questions
TalentJR

How to solve it (Factors come in pairs): Find factors in pairs: 1 × N, 2 × …, 3 × …, until the pairs meet. Prime factorisation: keep dividing by the smallest prime that works, then group equal primes as powers. 1 is not a prime; 2 is the only even prime. To test a number, try dividing by the primes up to its square root.

NameDateTime takenScore ___ / 40
  1. 1.How many factors does 22 have? (a) 3 (b) 5 (c) 4 (d) 2
  2. 2.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
  3. 3.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 5 (d) 3
  4. 4.How many factors does 113 have? (a) 4 (b) 1 (c) 2 (d) 3
  5. 5.How many factors does 117 have? (a) 5 (b) 4 (c) 7 (d) 6
  6. 6.How many factors does 86 have? (a) 4 (b) 3 (c) 5 (d) 2
  7. 7.How many factors does 46 have? (a) 4 (b) 3 (c) 5 (d) 2
  8. 8.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 7 (d) 13
  9. 9.What is the smallest prime factor of 203? (a) 29 (b) 1 (c) 2 (d) 7
  10. 10.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 13 (d) 11
  11. 11.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 2 (d) 31
  12. 12.How many factors does 95 have? (a) 3 (b) 4 (c) 2 (d) 5
  13. 13.How many prime numbers are there between 80 and 110? (a) 9 (b) 6 (c) 8 (d) 7
  14. 14.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7³
  15. 15.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2 × 7⁴
  16. 16.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
  17. 17.How many prime numbers are there between 50 and 60? (a) 2 (b) 1 (c) 4 (d) 3
  18. 18.How many factors does 36 have? (a) 9 (b) 7 (c) 8 (d) 10
  19. 19.How many factors does 13 have? (a) 1 (b) 3 (c) 2 (d) 4
  20. 20.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2⁴ × 7 (d) 2 × 7³
  21. 21.How many factors does 93 have? (a) 2 (b) 5 (c) 3 (d) 4
  22. 22.How many factors does 54 have? (a) 9 (b) 6 (c) 8 (d) 7
  23. 23.How many factors does 33 have? (a) 2 (b) 4 (c) 5 (d) 3
  24. 24.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 2 (d) 1
  25. 25.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
  26. 26.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
  27. 27.How many factors does 85 have? (a) 4 (b) 2 (c) 5 (d) 3
  28. 28.How many factors does 116 have? (a) 7 (b) 5 (c) 4 (d) 6
  29. 29.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 3 (d) 2
  30. 30.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 2 (d) 3
  31. 31.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 9 (d) 6
  32. 32.What is the prime factorisation of 28? (a) 2 × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2² × 7
  33. 33.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  34. 34.How many factors does 20 have? (a) 6 (b) 5 (c) 7 (d) 4
  35. 35.What is the smallest prime factor of 119? (a) 1 (b) 7 (c) 2 (d) 17
  36. 36.How many factors does 25 have? (a) 3 (b) 1 (c) 4 (d) 2
  37. 37.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 9 (d) 7
  38. 38.How many prime numbers are there between 60 and 70? (a) 4 (b) 3 (c) 1 (d) 2
  39. 39.How many factors does 80 have? (a) 8 (b) 10 (c) 9 (d) 11
  40. 40.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 3 (d) 1

Answer key

  1. 4
  2. 2⁴ × 5
  3. 4
  4. 2
  5. 6
  6. 4
  7. 4
  8. 7
  9. 7
  10. 11
  11. 3
  12. 4
  13. 7
  14. 2³ × 3² × 7
  15. 2⁴ × 7
  16. 3
  17. 2
  18. 9
  19. 2
  20. 2³ × 7
  21. 4
  22. 8
  23. 4
  24. 5
  25. 3 × 5
  26. 2³ × 3² × 5
  27. 4
  28. 6
  29. 3
  30. 1
  31. 7
  32. 2² × 7
  33. 2² × 3² × 5
  34. 6
  35. 7
  36. 3
  37. 7
  38. 2
  39. 10
  40. 3

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