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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 24 · 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 prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 7 (d) 6
  2. 2.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
  3. 3.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2⁴ × 7 (d) 2 × 7³
  4. 4.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 1 (d) 2
  5. 5.How many factors does 60 have? (a) 11 (b) 13 (c) 10 (d) 12
  6. 6.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
  7. 7.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5³ (d) 2⁴ × 3² × 5
  8. 8.How many factors does 103 have? (a) 3 (b) 4 (c) 2 (d) 1
  9. 9.How many factors does 70 have? (a) 8 (b) 9 (c) 6 (d) 7
  10. 10.How many factors does 119 have? (a) 2 (b) 4 (c) 5 (d) 3
  11. 11.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
  12. 12.How many prime numbers are there between 10 and 20? (a) 5 (b) 4 (c) 6 (d) 3
  13. 13.What is the smallest prime factor of 121? (a) 3 (b) 1 (c) 11 (d) 2
  14. 14.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 2 (d) 3
  15. 15.How many prime numbers are there between 40 and 60? (a) 7 (b) 6 (c) 5 (d) 4
  16. 16.How many factors does 89 have? (a) 1 (b) 4 (c) 3 (d) 2
  17. 17.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
  18. 18.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  19. 19.How many factors does 49 have? (a) 2 (b) 1 (c) 4 (d) 3
  20. 20.What is the prime factorisation of 28? (a) 2 × 7² (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7
  21. 21.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 2 (d) 4
  22. 22.What is the smallest prime factor of 155? (a) 31 (b) 1 (c) 5 (d) 2
  23. 23.How many factors does 17 have? (a) 2 (b) 1 (c) 4 (d) 3
  24. 24.How many factors does 59 have? (a) 1 (b) 3 (c) 4 (d) 2
  25. 25.How many prime numbers are there between 40 and 50? (a) 2 (b) 5 (c) 3 (d) 4
  26. 26.How many factors does 46 have? (a) 3 (b) 5 (c) 2 (d) 4
  27. 27.How many prime numbers are there between 60 and 70? (a) 1 (b) 4 (c) 3 (d) 2
  28. 28.How many prime numbers are there between 90 and 120? (a) 7 (b) 6 (c) 8 (d) 5
  29. 29.How many factors does 92 have? (a) 5 (b) 6 (c) 4 (d) 7
  30. 30.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7³ (d) 2³ × 3 × 7
  31. 31.How many prime numbers are there between 10 and 40? (a) 7 (b) 9 (c) 8 (d) 10
  32. 32.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5 (c) 2² × 5 (d) 2 × 5²
  33. 33.How many factors does 26 have? (a) 3 (b) 4 (c) 2 (d) 5
  34. 34.How many prime numbers are there between 70 and 80? (a) 3 (b) 5 (c) 2 (d) 4
  35. 35.How many factors does 83 have? (a) 2 (b) 1 (c) 3 (d) 4
  36. 36.How many factors does 77 have? (a) 5 (b) 2 (c) 4 (d) 3
  37. 37.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5 × 7
  38. 38.How many factors does 24 have? (a) 6 (b) 8 (c) 9 (d) 7
  39. 39.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
  40. 40.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2² × 3² (c) 2 × 3² (d) 2³ × 3²

Answer key

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

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