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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 64 · 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 factors does 95 have? (a) 4 (b) 5 (c) 3 (d) 2
  2. 2.How many factors does 18 have? (a) 7 (b) 6 (c) 4 (d) 5
  3. 3.How many factors does 99 have? (a) 5 (b) 7 (c) 4 (d) 6
  4. 4.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 9 (d) 7
  5. 5.How many factors does 63 have? (a) 4 (b) 5 (c) 7 (d) 6
  6. 6.How many factors does 79 have? (a) 1 (b) 4 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 4 (d) 3
  8. 8.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2
  9. 9.How many factors does 97 have? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.How many prime numbers are there between 80 and 110? (a) 8 (b) 6 (c) 7 (d) 9
  11. 11.How many factors does 93 have? (a) 5 (b) 2 (c) 3 (d) 4
  12. 12.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 3 (d) 4
  13. 13.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
  14. 14.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁴ × 5 (c) 2³ × 5 (d) 2⁵ × 5
  15. 15.What is the smallest prime factor of 133? (a) 7 (b) 19 (c) 2 (d) 1
  16. 16.What is the smallest prime factor of 57? (a) 1 (b) 3 (c) 2 (d) 19
  17. 17.How many factors does 77 have? (a) 3 (b) 4 (c) 2 (d) 5
  18. 18.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  19. 19.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2 × 3³ (d) 2² × 3²
  20. 20.What is the smallest prime factor of 119? (a) 2 (b) 7 (c) 1 (d) 17
  21. 21.How many factors does 74 have? (a) 3 (b) 4 (c) 5 (d) 2
  22. 22.What is the smallest prime factor of 203? (a) 2 (b) 29 (c) 1 (d) 7
  23. 23.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
  24. 24.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 4 (d) 1
  25. 25.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
  26. 26.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2² × 5 (d) 2³ × 5
  27. 27.How many factors does 73 have? (a) 1 (b) 4 (c) 3 (d) 2
  28. 28.What is the smallest prime factor of 69? (a) 3 (b) 2 (c) 1 (d) 23
  29. 29.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 13 (d) 5
  30. 30.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  31. 31.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 3 (d) 29
  32. 32.How many factors does 86 have? (a) 2 (b) 5 (c) 3 (d) 4
  33. 33.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3² × 5 × 7 (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  34. 34.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 2 (d) 1
  35. 35.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 1 (d) 17
  36. 36.What is the smallest prime factor of 253? (a) 23 (b) 11 (c) 2 (d) 1
  37. 37.How many prime numbers are there between 90 and 110? (a) 7 (b) 4 (c) 6 (d) 5
  38. 38.How many prime numbers are there between 50 and 80? (a) 6 (b) 9 (c) 7 (d) 8
  39. 39.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2³ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2⁴ × 5 × 7
  40. 40.How many factors does 37 have? (a) 4 (b) 1 (c) 3 (d) 2

Answer key

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

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