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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 108 · 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 prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2² × 3 × 7 (d) 2 × 3 × 7
  2. 2.How many factors does 67 have? (a) 3 (b) 4 (c) 1 (d) 2
  3. 3.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2 × 7² (d) 2³ × 7
  4. 4.What is the prime factorisation of 35? (a) 5 × 7² (b) 5² × 7 (c) 5 × 7 (d) 5³ × 7
  5. 5.How many factors does 17 have? (a) 1 (b) 4 (c) 2 (d) 3
  6. 6.How many factors does 119 have? (a) 4 (b) 5 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
  8. 8.How many factors does 25 have? (a) 2 (b) 3 (c) 4 (d) 1
  9. 9.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 2 (d) 5
  10. 10.What is the prime factorisation of 28? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  11. 11.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 1 (d) 7
  12. 12.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
  13. 13.How many factors does 28 have? (a) 6 (b) 5 (c) 7 (d) 4
  14. 14.How many factors does 61 have? (a) 2 (b) 4 (c) 1 (d) 3
  15. 15.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 4 (d) 5
  16. 16.What is the smallest prime factor of 403? (a) 13 (b) 2 (c) 31 (d) 1
  17. 17.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 1 (d) 11
  18. 18.How many factors does 42 have? (a) 6 (b) 7 (c) 8 (d) 9
  19. 19.What is the smallest prime factor of 21? (a) 1 (b) 7 (c) 3 (d) 2
  20. 20.How many factors does 102 have? (a) 9 (b) 6 (c) 7 (d) 8
  21. 21.What is the smallest prime factor of 57? (a) 3 (b) 1 (c) 2 (d) 19
  22. 22.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 29 (d) 11
  23. 23.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5³ (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  24. 24.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 5 (d) 17
  25. 25.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 2 (d) 4
  26. 26.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  27. 27.What is the smallest prime factor of 299? (a) 13 (b) 1 (c) 2 (d) 23
  28. 28.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2⁴ × 3² × 5 (c) 2³ × 3² × 5 (d) 2² × 3² × 5
  29. 29.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 8 (d) 9
  30. 30.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  31. 31.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 4 (d) 7
  32. 32.What is the smallest prime factor of 87? (a) 29 (b) 1 (c) 3 (d) 2
  33. 33.How many prime numbers are there between 80 and 90? (a) 2 (b) 4 (c) 3 (d) 1
  34. 34.How many factors does 62 have? (a) 3 (b) 4 (c) 5 (d) 2
  35. 35.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 11 (d) 2
  36. 36.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2³ × 3² × 5
  37. 37.How many factors does 35 have? (a) 5 (b) 4 (c) 3 (d) 2
  38. 38.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  39. 39.What is the smallest prime factor of 133? (a) 7 (b) 19 (c) 1 (d) 2
  40. 40.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 31 (d) 1

Answer key

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

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