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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 216 · 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 34 have? (a) 4 (b) 2 (c) 3 (d) 5
  2. 2.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 29 (d) 2
  3. 3.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2² × 5 (d) 2³ × 5
  4. 4.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 7 (d) 6
  5. 5.What is the smallest prime factor of 121? (a) 11 (b) 3 (c) 2 (d) 1
  6. 6.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 2 (d) 4
  7. 7.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
  8. 8.How many prime numbers are there between 90 and 120? (a) 7 (b) 6 (c) 8 (d) 5
  9. 9.How many factors does 53 have? (a) 4 (b) 3 (c) 1 (d) 2
  10. 10.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 1 (d) 3
  11. 11.What is the prime factorisation of 28? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2 × 7
  12. 12.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2⁵ × 5 (c) 2³ × 5 (d) 2 × 5⁴
  13. 13.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  14. 14.How many factors does 28 have? (a) 5 (b) 7 (c) 6 (d) 4
  15. 15.How many factors does 59 have? (a) 1 (b) 4 (c) 2 (d) 3
  16. 16.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5³ (d) 2³ × 3 × 5
  17. 17.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  18. 18.How many factors does 83 have? (a) 4 (b) 1 (c) 3 (d) 2
  19. 19.How many factors does 65 have? (a) 2 (b) 3 (c) 5 (d) 4
  20. 20.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2² × 3 (d) 2³ × 3
  21. 21.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2³ × 3 (d) 2⁴ × 3
  22. 22.How many factors does 38 have? (a) 2 (b) 4 (c) 5 (d) 3
  23. 23.How many factors does 73 have? (a) 2 (b) 3 (c) 1 (d) 4
  24. 24.How many prime numbers are there between 40 and 60? (a) 4 (b) 6 (c) 5 (d) 7
  25. 25.How many factors does 24 have? (a) 8 (b) 6 (c) 9 (d) 7
  26. 26.How many factors does 36 have? (a) 8 (b) 9 (c) 10 (d) 7
  27. 27.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 5 (d) 7
  28. 28.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 3 (d) 2
  29. 29.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 9 (d) 7
  30. 30.How many prime numbers are there between 90 and 110? (a) 4 (b) 7 (c) 6 (d) 5
  31. 31.How many factors does 63 have? (a) 7 (b) 4 (c) 6 (d) 5
  32. 32.What is the smallest prime factor of 403? (a) 13 (b) 31 (c) 2 (d) 1
  33. 33.How many factors does 95 have? (a) 4 (b) 3 (c) 5 (d) 2
  34. 34.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 3 (d) 1
  35. 35.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 8 (d) 9
  36. 36.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
  37. 37.How many factors does 29 have? (a) 2 (b) 4 (c) 3 (d) 1
  38. 38.How many factors does 35 have? (a) 3 (b) 2 (c) 4 (d) 5
  39. 39.What is the smallest prime factor of 377? (a) 1 (b) 29 (c) 2 (d) 13
  40. 40.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2 × 3² (d) 2² × 3

Answer key

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

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