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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 165 · 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 70 and 100? (a) 6 (b) 8 (c) 5 (d) 7
  2. 2.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 6 (d) 7
  3. 3.How many factors does 36 have? (a) 8 (b) 10 (c) 9 (d) 7
  4. 4.How many factors does 33 have? (a) 5 (b) 3 (c) 4 (d) 2
  5. 5.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2 × 3 × 5³ (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
  6. 6.How many factors does 42 have? (a) 8 (b) 7 (c) 9 (d) 6
  7. 7.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
  8. 8.How many factors does 79 have? (a) 3 (b) 1 (c) 4 (d) 2
  9. 9.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2
  10. 10.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 29 (d) 2
  11. 11.How many factors does 120 have? (a) 15 (b) 14 (c) 16 (d) 17
  12. 12.How many factors does 80 have? (a) 8 (b) 10 (c) 9 (d) 11
  13. 13.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 1 (d) 11
  14. 14.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 11 (d) 1
  15. 15.What is the smallest prime factor of 91? (a) 2 (b) 7 (c) 1 (d) 13
  16. 16.What is the prime factorisation of 15? (a) 3 × 5 (b) 3² × 5 (c) 3 × 5² (d) 3³ × 5
  17. 17.How many prime numbers are there between 50 and 80? (a) 9 (b) 8 (c) 6 (d) 7
  18. 18.How many factors does 55 have? (a) 3 (b) 2 (c) 5 (d) 4
  19. 19.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  20. 20.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
  21. 21.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 2 (d) 5
  22. 22.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 6 (d) 7
  23. 23.How many factors does 115 have? (a) 3 (b) 4 (c) 5 (d) 2
  24. 24.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2⁵ × 3² (c) 2² × 3⁴ (d) 2³ × 3²
  25. 25.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2 × 3² × 7 (d) 2³ × 3² × 7
  26. 26.What is the smallest prime factor of 55? (a) 5 (b) 2 (c) 11 (d) 1
  27. 27.How many factors does 109 have? (a) 3 (b) 2 (c) 1 (d) 4
  28. 28.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 2 (d) 0
  29. 29.How many factors does 38 have? (a) 2 (b) 3 (c) 5 (d) 4
  30. 30.How many prime numbers are there between 70 and 90? (a) 4 (b) 5 (c) 7 (d) 6
  31. 31.What is the smallest prime factor of 203? (a) 1 (b) 29 (c) 7 (d) 2
  32. 32.How many factors does 59 have? (a) 1 (b) 3 (c) 4 (d) 2
  33. 33.How many factors does 86 have? (a) 3 (b) 4 (c) 2 (d) 5
  34. 34.What is the smallest prime factor of 377? (a) 2 (b) 1 (c) 13 (d) 29
  35. 35.How many factors does 17 have? (a) 3 (b) 2 (c) 4 (d) 1
  36. 36.How many factors does 24 have? (a) 8 (b) 7 (c) 6 (d) 9
  37. 37.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 5 (d) 3
  38. 38.How many prime numbers are there between 60 and 80? (a) 4 (b) 5 (c) 6 (d) 7
  39. 39.How many factors does 58 have? (a) 3 (b) 4 (c) 2 (d) 5
  40. 40.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 5 (d) 1

Answer key

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

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