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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 101 · 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 90? (a) 7 (b) 5 (c) 4 (d) 6
  2. 2.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  3. 3.What is the smallest prime factor of 55? (a) 2 (b) 1 (c) 11 (d) 5
  4. 4.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  5. 5.What is the smallest prime factor of 169? (a) 1 (b) 13 (c) 2 (d) 3
  6. 6.How many factors does 35 have? (a) 2 (b) 5 (c) 4 (d) 3
  7. 7.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 5 (d) 2
  8. 8.What is the smallest prime factor of 203? (a) 1 (b) 7 (c) 2 (d) 29
  9. 9.What is the smallest prime factor of 247? (a) 13 (b) 1 (c) 2 (d) 19
  10. 10.How many factors does 70 have? (a) 9 (b) 7 (c) 6 (d) 8
  11. 11.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2 × 3²
  12. 12.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 4 (d) 3
  13. 13.What is the prime factorisation of 35? (a) 5 × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5² × 7
  14. 14.How many factors does 116 have? (a) 4 (b) 6 (c) 7 (d) 5
  15. 15.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2³ × 5
  16. 16.What is the smallest prime factor of 85? (a) 17 (b) 1 (c) 5 (d) 2
  17. 17.What is the smallest prime factor of 121? (a) 11 (b) 1 (c) 2 (d) 3
  18. 18.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3³ (d) 2⁴ × 3
  19. 19.How many factors does 29 have? (a) 2 (b) 3 (c) 4 (d) 1
  20. 20.What is the smallest prime factor of 57? (a) 2 (b) 1 (c) 3 (d) 19
  21. 21.How many factors does 58 have? (a) 5 (b) 3 (c) 4 (d) 2
  22. 22.How many factors does 71 have? (a) 3 (b) 4 (c) 2 (d) 1
  23. 23.How many factors does 108 have? (a) 13 (b) 12 (c) 11 (d) 10
  24. 24.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3 × 5² (d) 3³ × 5
  25. 25.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
  26. 26.How many factors does 13 have? (a) 4 (b) 3 (c) 2 (d) 1
  27. 27.How many factors does 34 have? (a) 5 (b) 3 (c) 2 (d) 4
  28. 28.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 23 (d) 13
  29. 29.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 1 (d) 11
  30. 30.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2⁵ × 3 × 7
  31. 31.What is the prime factorisation of 63? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
  32. 32.What is the smallest prime factor of 49? (a) 3 (b) 7 (c) 1 (d) 2
  33. 33.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 5 (d) 7
  34. 34.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 3 (d) 5
  35. 35.What is the smallest prime factor of 145? (a) 1 (b) 2 (c) 5 (d) 29
  36. 36.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7³ (d) 2³ × 3 × 7
  37. 37.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 6 (d) 8
  38. 38.How many factors does 47 have? (a) 1 (b) 4 (c) 3 (d) 2
  39. 39.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 6 (d) 7
  40. 40.How many prime numbers are there between 10 and 40? (a) 10 (b) 9 (c) 7 (d) 8

Answer key

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

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