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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 79 · 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 80 and 90? (a) 2 (b) 1 (c) 4 (d) 3
  2. 2.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 4 (d) 5
  3. 3.How many factors does 38 have? (a) 2 (b) 3 (c) 4 (d) 5
  4. 4.How many prime numbers are there between 70 and 100? (a) 6 (b) 8 (c) 7 (d) 5
  5. 5.How many factors does 95 have? (a) 3 (b) 4 (c) 5 (d) 2
  6. 6.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  7. 7.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 3 (d) 1
  8. 8.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁵ × 3 × 5
  9. 9.What is the smallest prime factor of 35? (a) 2 (b) 7 (c) 5 (d) 1
  10. 10.How many factors does 56 have? (a) 9 (b) 7 (c) 6 (d) 8
  11. 11.How many factors does 71 have? (a) 2 (b) 3 (c) 1 (d) 4
  12. 12.How many factors does 113 have? (a) 4 (b) 2 (c) 1 (d) 3
  13. 13.How many factors does 48 have? (a) 11 (b) 9 (c) 8 (d) 10
  14. 14.How many factors does 108 have? (a) 11 (b) 13 (c) 10 (d) 12
  15. 15.What is the prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7
  16. 16.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2² × 3² (d) 2 × 3³
  17. 17.How many factors does 109 have? (a) 4 (b) 1 (c) 3 (d) 2
  18. 18.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  19. 19.How many factors does 119 have? (a) 5 (b) 4 (c) 2 (d) 3
  20. 20.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
  21. 21.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2³ × 3²
  22. 22.How many factors does 15 have? (a) 5 (b) 3 (c) 2 (d) 4
  23. 23.How many factors does 76 have? (a) 5 (b) 4 (c) 7 (d) 6
  24. 24.What is the smallest prime factor of 133? (a) 2 (b) 1 (c) 19 (d) 7
  25. 25.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 1 (d) 11
  26. 26.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 4 (d) 3
  27. 27.What is the smallest prime factor of 341? (a) 11 (b) 2 (c) 1 (d) 31
  28. 28.How many factors does 101 have? (a) 1 (b) 3 (c) 4 (d) 2
  29. 29.How many factors does 13 have? (a) 1 (b) 3 (c) 2 (d) 4
  30. 30.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 4 (d) 3
  31. 31.What is the smallest prime factor of 85? (a) 17 (b) 1 (c) 2 (d) 5
  32. 32.What is the smallest prime factor of 253? (a) 11 (b) 23 (c) 1 (d) 2
  33. 33.How many factors does 58 have? (a) 3 (b) 5 (c) 4 (d) 2
  34. 34.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  35. 35.How many factors does 116 have? (a) 5 (b) 4 (c) 7 (d) 6
  36. 36.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
  37. 37.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
  38. 38.How many factors does 52 have? (a) 4 (b) 7 (c) 5 (d) 6
  39. 39.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
  40. 40.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2

Answer key

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

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