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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 129 · 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.What is the smallest prime factor of 33? (a) 1 (b) 3 (c) 2 (d) 11
  2. 2.How many factors does 24 have? (a) 6 (b) 7 (c) 9 (d) 8
  3. 3.How many prime numbers are there between 70 and 100? (a) 8 (b) 5 (c) 6 (d) 7
  4. 4.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 1 (d) 2
  5. 5.What is the smallest prime factor of 21? (a) 2 (b) 3 (c) 1 (d) 7
  6. 6.How many prime numbers are there between 80 and 110? (a) 9 (b) 8 (c) 7 (d) 6
  7. 7.What is the prime factorisation of 15? (a) 3 × 5² (b) 3³ × 5 (c) 3 × 5 (d) 3² × 5
  8. 8.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
  9. 9.How many factors does 96 have? (a) 12 (b) 13 (c) 11 (d) 10
  10. 10.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 7 (d) 9
  11. 11.How many factors does 14 have? (a) 4 (b) 5 (c) 3 (d) 2
  12. 12.What is the smallest prime factor of 403? (a) 1 (b) 31 (c) 2 (d) 13
  13. 13.What is the smallest prime factor of 87? (a) 29 (b) 2 (c) 3 (d) 1
  14. 14.How many factors does 91 have? (a) 5 (b) 4 (c) 2 (d) 3
  15. 15.How many factors does 88 have? (a) 9 (b) 8 (c) 6 (d) 7
  16. 16.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  17. 17.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 2 (d) 1
  18. 18.How many factors does 97 have? (a) 4 (b) 1 (c) 3 (d) 2
  19. 19.How many prime numbers are there between 50 and 80? (a) 6 (b) 7 (c) 9 (d) 8
  20. 20.How many factors does 67 have? (a) 4 (b) 2 (c) 3 (d) 1
  21. 21.What is the smallest prime factor of 39? (a) 3 (b) 2 (c) 1 (d) 13
  22. 22.What is the prime factorisation of 12? (a) 2² × 3 (b) 2 × 3 (c) 2 × 3² (d) 2³ × 3
  23. 23.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 4 (d) 6
  24. 24.How many prime numbers are there between 90 and 100? (a) 0 (b) 2 (c) 1 (d) 3
  25. 25.How many factors does 19 have? (a) 4 (b) 3 (c) 1 (d) 2
  26. 26.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 4 (d) 5
  27. 27.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 4 (d) 3
  28. 28.How many factors does 36 have? (a) 9 (b) 10 (c) 7 (d) 8
  29. 29.How many prime numbers are there between 30 and 60? (a) 9 (b) 6 (c) 7 (d) 8
  30. 30.How many factors does 103 have? (a) 1 (b) 2 (c) 3 (d) 4
  31. 31.How many prime numbers are there between 90 and 120? (a) 6 (b) 8 (c) 5 (d) 7
  32. 32.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 1 (d) 2
  33. 33.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
  34. 34.How many factors does 98 have? (a) 7 (b) 4 (c) 5 (d) 6
  35. 35.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2 × 3² × 7
  36. 36.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2² × 3 × 7
  37. 37.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2² × 3 × 5
  38. 38.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 3 (d) 1
  39. 39.How many factors does 39 have? (a) 3 (b) 5 (c) 4 (d) 2
  40. 40.How many factors does 21 have? (a) 4 (b) 5 (c) 2 (d) 3

Answer key

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

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