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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 76 · 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 90 and 120? (a) 7 (b) 6 (c) 5 (d) 8
  2. 2.How many factors does 66 have? (a) 9 (b) 6 (c) 8 (d) 7
  3. 3.What is the smallest prime factor of 121? (a) 11 (b) 2 (c) 3 (d) 1
  4. 4.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2⁴ × 3 × 5
  5. 5.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 2 (d) 17
  6. 6.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2³ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
  7. 7.How many factors does 36 have? (a) 9 (b) 10 (c) 7 (d) 8
  8. 8.How many factors does 75 have? (a) 5 (b) 4 (c) 6 (d) 7
  9. 9.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.How many prime numbers are there between 80 and 90? (a) 1 (b) 2 (c) 4 (d) 3
  11. 11.How many factors does 12 have? (a) 6 (b) 4 (c) 5 (d) 7
  12. 12.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2² × 3
  13. 13.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3³ (c) 2³ × 3² (d) 2² × 3²
  14. 14.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
  15. 15.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
  16. 16.How many factors does 30 have? (a) 9 (b) 7 (c) 6 (d) 8
  17. 17.How many factors does 31 have? (a) 2 (b) 3 (c) 1 (d) 4
  18. 18.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7 (c) 3 × 7² (d) 3² × 7
  19. 19.How many factors does 24 have? (a) 8 (b) 6 (c) 9 (d) 7
  20. 20.How many prime numbers are there between 60 and 90? (a) 8 (b) 9 (c) 7 (d) 6
  21. 21.What is the smallest prime factor of 145? (a) 29 (b) 2 (c) 5 (d) 1
  22. 22.How many factors does 47 have? (a) 4 (b) 3 (c) 2 (d) 1
  23. 23.How many factors does 104 have? (a) 9 (b) 6 (c) 8 (d) 7
  24. 24.What is the smallest prime factor of 169? (a) 2 (b) 3 (c) 1 (d) 13
  25. 25.What is the smallest prime factor of 69? (a) 23 (b) 1 (c) 3 (d) 2
  26. 26.How many factors does 81 have? (a) 4 (b) 6 (c) 5 (d) 3
  27. 27.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 7 (d) 1
  28. 28.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
  29. 29.How many factors does 102 have? (a) 9 (b) 6 (c) 7 (d) 8
  30. 30.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2³ × 3² × 5
  31. 31.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2³ × 3 × 7 (d) 2² × 3 × 7
  32. 32.What is the smallest prime factor of 35? (a) 5 (b) 1 (c) 2 (d) 7
  33. 33.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 1 (d) 2
  34. 34.What is the smallest prime factor of 95? (a) 19 (b) 1 (c) 2 (d) 5
  35. 35.What is the smallest prime factor of 33? (a) 2 (b) 11 (c) 1 (d) 3
  36. 36.How many factors does 28 have? (a) 5 (b) 4 (c) 6 (d) 7
  37. 37.How many prime numbers are there between 30 and 50? (a) 6 (b) 7 (c) 4 (d) 5
  38. 38.How many prime numbers are there between 50 and 60? (a) 4 (b) 3 (c) 1 (d) 2
  39. 39.How many prime numbers are there between 20 and 40? (a) 4 (b) 3 (c) 5 (d) 6
  40. 40.What is the smallest prime factor of 57? (a) 19 (b) 3 (c) 1 (d) 2

Answer key

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

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