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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 89 · 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 40 and 60? (a) 4 (b) 6 (c) 5 (d) 7
  2. 2.What is the prime factorisation of 45? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
  3. 3.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
  4. 4.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 4 (d) 1
  5. 5.How many factors does 55 have? (a) 5 (b) 3 (c) 2 (d) 4
  6. 6.How many factors does 31 have? (a) 2 (b) 1 (c) 4 (d) 3
  7. 7.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2² × 5 × 7
  8. 8.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 3 (d) 4
  9. 9.How many factors does 78 have? (a) 8 (b) 6 (c) 7 (d) 9
  10. 10.How many prime numbers are there between 60 and 80? (a) 4 (b) 6 (c) 7 (d) 5
  11. 11.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  12. 12.How many factors does 12 have? (a) 4 (b) 6 (c) 7 (d) 5
  13. 13.How many factors does 45 have? (a) 6 (b) 7 (c) 4 (d) 5
  14. 14.What is the smallest prime factor of 87? (a) 3 (b) 29 (c) 1 (d) 2
  15. 15.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 9 (d) 8
  16. 16.How many factors does 26 have? (a) 5 (b) 4 (c) 2 (d) 3
  17. 17.How many factors does 112 have? (a) 9 (b) 11 (c) 10 (d) 8
  18. 18.How many factors does 69 have? (a) 3 (b) 5 (c) 2 (d) 4
  19. 19.How many factors does 116 have? (a) 5 (b) 6 (c) 4 (d) 7
  20. 20.How many prime numbers are there between 70 and 90? (a) 6 (b) 7 (c) 4 (d) 5
  21. 21.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  22. 22.How many factors does 96 have? (a) 10 (b) 12 (c) 13 (d) 11
  23. 23.What is the smallest prime factor of 145? (a) 2 (b) 29 (c) 1 (d) 5
  24. 24.How many prime numbers are there between 90 and 100? (a) 3 (b) 2 (c) 1 (d) 0
  25. 25.How many prime numbers are there between 20 and 50? (a) 7 (b) 9 (c) 8 (d) 6
  26. 26.How many factors does 30 have? (a) 8 (b) 6 (c) 7 (d) 9
  27. 27.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2³ × 5
  28. 28.How many factors does 20 have? (a) 5 (b) 6 (c) 4 (d) 7
  29. 29.What is the smallest prime factor of 403? (a) 2 (b) 13 (c) 1 (d) 31
  30. 30.How many factors does 94 have? (a) 5 (b) 2 (c) 4 (d) 3
  31. 31.How many factors does 111 have? (a) 3 (b) 2 (c) 4 (d) 5
  32. 32.What is the smallest prime factor of 217? (a) 2 (b) 7 (c) 1 (d) 31
  33. 33.How many prime numbers are there between 30 and 60? (a) 9 (b) 8 (c) 6 (d) 7
  34. 34.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 1 (d) 2
  35. 35.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2⁴ × 3 × 5
  36. 36.How many factors does 52 have? (a) 4 (b) 5 (c) 7 (d) 6
  37. 37.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3² (d) 2 × 3
  38. 38.What is the smallest prime factor of 55? (a) 1 (b) 11 (c) 2 (d) 5
  39. 39.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  40. 40.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 6 (d) 9

Answer key

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

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