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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 32 · 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 100? (a) 5 (b) 2 (c) 3 (d) 4
  2. 2.How many factors does 53 have? (a) 4 (b) 3 (c) 1 (d) 2
  3. 3.How many prime numbers are there between 40 and 50? (a) 5 (b) 2 (c) 4 (d) 3
  4. 4.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 5 (d) 3
  5. 5.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
  6. 6.How many factors does 117 have? (a) 4 (b) 6 (c) 5 (d) 7
  7. 7.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 6 (d) 9
  8. 8.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  9. 9.What is the smallest prime factor of 319? (a) 2 (b) 1 (c) 11 (d) 29
  10. 10.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  11. 11.How many factors does 98 have? (a) 4 (b) 5 (c) 7 (d) 6
  12. 12.How many factors does 112 have? (a) 8 (b) 10 (c) 9 (d) 11
  13. 13.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  14. 14.What is the smallest prime factor of 155? (a) 2 (b) 5 (c) 31 (d) 1
  15. 15.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2³ × 3 × 7
  16. 16.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
  17. 17.How many factors does 99 have? (a) 7 (b) 6 (c) 5 (d) 4
  18. 18.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2⁴ × 3 (d) 2³ × 3
  19. 19.How many factors does 74 have? (a) 3 (b) 5 (c) 2 (d) 4
  20. 20.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 4 (d) 6
  21. 21.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 1 (d) 2
  22. 22.What is the prime factorisation of 18? (a) 2 × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2² × 3²
  23. 23.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5 × 7 (d) 5³ × 7
  24. 24.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2⁴ × 7 (d) 2 × 7³
  25. 25.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 7 (d) 5
  26. 26.How many factors does 114 have? (a) 7 (b) 8 (c) 6 (d) 9
  27. 27.What is the smallest prime factor of 35? (a) 1 (b) 2 (c) 5 (d) 7
  28. 28.How many factors does 20 have? (a) 7 (b) 4 (c) 6 (d) 5
  29. 29.How many prime numbers are there between 50 and 70? (a) 4 (b) 5 (c) 6 (d) 3
  30. 30.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2 × 3² × 7
  31. 31.How many factors does 71 have? (a) 2 (b) 3 (c) 1 (d) 4
  32. 32.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 3 (d) 2
  33. 33.How many factors does 108 have? (a) 12 (b) 13 (c) 11 (d) 10
  34. 34.How many factors does 57 have? (a) 2 (b) 5 (c) 3 (d) 4
  35. 35.How many factors does 119 have? (a) 3 (b) 2 (c) 4 (d) 5
  36. 36.How many factors does 68 have? (a) 7 (b) 5 (c) 6 (d) 4
  37. 37.What is the prime factorisation of 63? (a) 3² × 7 (b) 3 × 7² (c) 3 × 7 (d) 3³ × 7
  38. 38.How many factors does 25 have? (a) 3 (b) 2 (c) 4 (d) 1
  39. 39.What is the smallest prime factor of 247? (a) 13 (b) 1 (c) 2 (d) 19
  40. 40.How many factors does 30 have? (a) 7 (b) 8 (c) 9 (d) 6

Answer key

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

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