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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 9 · 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 60? (a) 8 (b) 6 (c) 7 (d) 9
  2. 2.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 1 (d) 3
  3. 3.How many factors does 24 have? (a) 7 (b) 6 (c) 9 (d) 8
  4. 4.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 6 (d) 5
  5. 5.What is the smallest prime factor of 209? (a) 11 (b) 2 (c) 1 (d) 19
  6. 6.How many factors does 90 have? (a) 13 (b) 11 (c) 12 (d) 10
  7. 7.What is the smallest prime factor of 319? (a) 2 (b) 29 (c) 11 (d) 1
  8. 8.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 2 (d) 5
  9. 9.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
  10. 10.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 2 (d) 3
  11. 11.How many factors does 89 have? (a) 3 (b) 1 (c) 2 (d) 4
  12. 12.What is the smallest prime factor of 217? (a) 7 (b) 2 (c) 31 (d) 1
  13. 13.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 6 (d) 4
  14. 14.How many factors does 111 have? (a) 5 (b) 4 (c) 2 (d) 3
  15. 15.How many factors does 60 have? (a) 12 (b) 10 (c) 11 (d) 13
  16. 16.What is the smallest prime factor of 95? (a) 2 (b) 19 (c) 1 (d) 5
  17. 17.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 4 (d) 3
  18. 18.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 3 (d) 5
  19. 19.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  20. 20.How many factors does 116 have? (a) 6 (b) 4 (c) 5 (d) 7
  21. 21.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
  22. 22.How many prime numbers are there between 70 and 90? (a) 4 (b) 6 (c) 7 (d) 5
  23. 23.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
  24. 24.What is the smallest prime factor of 119? (a) 17 (b) 7 (c) 2 (d) 1
  25. 25.How many prime numbers are there between 50 and 80? (a) 7 (b) 9 (c) 8 (d) 6
  26. 26.How many factors does 35 have? (a) 4 (b) 5 (c) 3 (d) 2
  27. 27.How many factors does 76 have? (a) 5 (b) 6 (c) 4 (d) 7
  28. 28.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 4 (d) 3
  29. 29.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 8 (d) 9
  30. 30.How many factors does 38 have? (a) 4 (b) 3 (c) 2 (d) 5
  31. 31.How many factors does 70 have? (a) 6 (b) 7 (c) 9 (d) 8
  32. 32.How many factors does 17 have? (a) 3 (b) 2 (c) 4 (d) 1
  33. 33.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
  34. 34.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2⁴ × 3 × 5
  35. 35.What is the smallest prime factor of 377? (a) 2 (b) 29 (c) 1 (d) 13
  36. 36.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 8 (d) 6
  37. 37.What is the smallest prime factor of 65? (a) 5 (b) 13 (c) 1 (d) 2
  38. 38.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 17 (d) 2
  39. 39.How many factors does 43 have? (a) 4 (b) 3 (c) 1 (d) 2
  40. 40.What is the smallest prime factor of 133? (a) 7 (b) 2 (c) 1 (d) 19

Answer key

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

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