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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 33 · 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 50 and 70? (a) 6 (b) 4 (c) 5 (d) 3
  2. 2.What is the smallest prime factor of 161? (a) 1 (b) 2 (c) 7 (d) 23
  3. 3.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2² × 3² × 7
  4. 4.How many factors does 76 have? (a) 5 (b) 6 (c) 7 (d) 4
  5. 5.How many factors does 46 have? (a) 4 (b) 5 (c) 2 (d) 3
  6. 6.How many prime numbers are there between 90 and 120? (a) 8 (b) 5 (c) 6 (d) 7
  7. 7.How many factors does 87 have? (a) 4 (b) 2 (c) 5 (d) 3
  8. 8.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 9 (d) 7
  9. 9.What is the smallest prime factor of 203? (a) 29 (b) 7 (c) 2 (d) 1
  10. 10.How many factors does 95 have? (a) 5 (b) 4 (c) 3 (d) 2
  11. 11.How many factors does 55 have? (a) 2 (b) 4 (c) 5 (d) 3
  12. 12.How many factors does 81 have? (a) 6 (b) 5 (c) 3 (d) 4
  13. 13.How many factors does 60 have? (a) 11 (b) 12 (c) 10 (d) 13
  14. 14.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 3 (d) 4
  15. 15.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  16. 16.How many prime numbers are there between 50 and 60? (a) 1 (b) 2 (c) 3 (d) 4
  17. 17.How many factors does 103 have? (a) 1 (b) 3 (c) 4 (d) 2
  18. 18.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2⁴ × 3²
  19. 19.How many factors does 17 have? (a) 2 (b) 1 (c) 4 (d) 3
  20. 20.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5⁴
  21. 21.What is the smallest prime factor of 209? (a) 19 (b) 1 (c) 11 (d) 2
  22. 22.How many factors does 83 have? (a) 2 (b) 1 (c) 3 (d) 4
  23. 23.How many factors does 43 have? (a) 4 (b) 3 (c) 2 (d) 1
  24. 24.How many factors does 52 have? (a) 7 (b) 6 (c) 5 (d) 4
  25. 25.What is the smallest prime factor of 253? (a) 11 (b) 2 (c) 23 (d) 1
  26. 26.What is the smallest prime factor of 85? (a) 1 (b) 5 (c) 2 (d) 17
  27. 27.How many factors does 35 have? (a) 3 (b) 5 (c) 2 (d) 4
  28. 28.How many factors does 58 have? (a) 4 (b) 5 (c) 2 (d) 3
  29. 29.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2² × 7 (d) 2³ × 7
  30. 30.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 3 (d) 4
  31. 31.What is the smallest prime factor of 169? (a) 13 (b) 1 (c) 3 (d) 2
  32. 32.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 6 (d) 8
  33. 33.What is the prime factorisation of 15? (a) 3 × 5 (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5²
  34. 34.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 4 (d) 6
  35. 35.How many factors does 114 have? (a) 9 (b) 6 (c) 7 (d) 8
  36. 36.What is the prime factorisation of 20? (a) 2 × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5²
  37. 37.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2² × 3 (c) 2⁴ × 3 (d) 2 × 3³
  38. 38.What is the smallest prime factor of 51? (a) 2 (b) 1 (c) 3 (d) 17
  39. 39.How many factors does 85 have? (a) 5 (b) 3 (c) 4 (d) 2
  40. 40.How many factors does 63 have? (a) 7 (b) 5 (c) 4 (d) 6

Answer key

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

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