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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 55 · 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 155? (a) 5 (b) 2 (c) 31 (d) 1
  2. 2.How many factors does 41 have? (a) 3 (b) 2 (c) 4 (d) 1
  3. 3.How many factors does 18 have? (a) 7 (b) 6 (c) 4 (d) 5
  4. 4.How many factors does 24 have? (a) 9 (b) 8 (c) 6 (d) 7
  5. 5.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 2 (d) 4
  6. 6.How many factors does 93 have? (a) 4 (b) 5 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
  8. 8.What is the smallest prime factor of 77? (a) 1 (b) 7 (c) 2 (d) 11
  9. 9.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5² (c) 2 × 5 (d) 2³ × 5
  10. 10.How many prime numbers are there between 90 and 120? (a) 6 (b) 5 (c) 7 (d) 8
  11. 11.How many factors does 40 have? (a) 9 (b) 6 (c) 8 (d) 7
  12. 12.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 3 (d) 11
  13. 13.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 4 (d) 6
  14. 14.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2² × 3² (c) 2³ × 3² (d) 2⁴ × 3²
  15. 15.How many factors does 66 have? (a) 8 (b) 6 (c) 9 (d) 7
  16. 16.How many prime numbers are there between 50 and 70? (a) 3 (b) 4 (c) 5 (d) 6
  17. 17.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 2 (d) 5
  18. 18.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 5 (d) 1
  19. 19.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  20. 20.How many factors does 47 have? (a) 1 (b) 3 (c) 4 (d) 2
  21. 21.How many factors does 113 have? (a) 4 (b) 3 (c) 1 (d) 2
  22. 22.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 1 (d) 4
  23. 23.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
  24. 24.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 8 (d) 6
  25. 25.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2⁴ × 3
  26. 26.How many factors does 92 have? (a) 5 (b) 4 (c) 7 (d) 6
  27. 27.What is the smallest prime factor of 35? (a) 7 (b) 5 (c) 1 (d) 2
  28. 28.How many factors does 32 have? (a) 5 (b) 7 (c) 6 (d) 4
  29. 29.How many prime numbers are there between 90 and 100? (a) 3 (b) 0 (c) 1 (d) 2
  30. 30.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3 × 5
  31. 31.How many factors does 108 have? (a) 11 (b) 10 (c) 12 (d) 13
  32. 32.What is the smallest prime factor of 121? (a) 11 (b) 3 (c) 2 (d) 1
  33. 33.How many factors does 62 have? (a) 2 (b) 3 (c) 5 (d) 4
  34. 34.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 8 (d) 7
  35. 35.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7² (c) 2 × 7 (d) 2² × 7
  36. 36.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 1 (d) 2
  37. 37.How many factors does 104 have? (a) 7 (b) 6 (c) 9 (d) 8
  38. 38.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 9 (d) 6
  39. 39.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  40. 40.What is the prime factorisation of 36? (a) 2² × 3² (b) 2³ × 3² (c) 2 × 3² (d) 2² × 3³

Answer key

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

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