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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 202 · 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 80 and 100? (a) 2 (b) 5 (c) 3 (d) 4
  2. 2.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 2 (d) 3
  3. 3.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2 × 3² (c) 2² × 3 (d) 2² × 3²
  4. 4.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  5. 5.How many factors does 107 have? (a) 1 (b) 3 (c) 2 (d) 4
  6. 6.How many factors does 13 have? (a) 1 (b) 4 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 1 (d) 2
  8. 8.What is the smallest prime factor of 253? (a) 23 (b) 2 (c) 11 (d) 1
  9. 9.How many factors does 12 have? (a) 6 (b) 4 (c) 5 (d) 7
  10. 10.How many factors does 53 have? (a) 2 (b) 3 (c) 1 (d) 4
  11. 11.How many factors does 36 have? (a) 10 (b) 7 (c) 8 (d) 9
  12. 12.What is the smallest prime factor of 55? (a) 2 (b) 5 (c) 11 (d) 1
  13. 13.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 9 (d) 8
  14. 14.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
  15. 15.How many factors does 86 have? (a) 5 (b) 3 (c) 4 (d) 2
  16. 16.How many factors does 110 have? (a) 8 (b) 7 (c) 6 (d) 9
  17. 17.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 2 (d) 31
  18. 18.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2³ × 3 × 5
  19. 19.How many factors does 102 have? (a) 7 (b) 6 (c) 8 (d) 9
  20. 20.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 7 (d) 10
  21. 21.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 8 (d) 6
  22. 22.What is the smallest prime factor of 203? (a) 1 (b) 7 (c) 29 (d) 2
  23. 23.How many factors does 16 have? (a) 3 (b) 5 (c) 4 (d) 6
  24. 24.What is the smallest prime factor of 69? (a) 2 (b) 1 (c) 23 (d) 3
  25. 25.What is the smallest prime factor of 35? (a) 5 (b) 2 (c) 1 (d) 7
  26. 26.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  27. 27.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 3 (d) 2
  28. 28.How many prime numbers are there between 60 and 70? (a) 1 (b) 3 (c) 4 (d) 2
  29. 29.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2 × 3² × 5² (c) 2³ × 3² × 5 (d) 2² × 3² × 5
  30. 30.What is the prime factorisation of 35? (a) 5 × 7 (b) 5³ × 7 (c) 5² × 7 (d) 5 × 7²
  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.How many factors does 50 have? (a) 4 (b) 6 (c) 7 (d) 5
  33. 33.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
  34. 34.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 6 (d) 4
  35. 35.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2
  36. 36.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 4 (d) 3
  37. 37.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 9 (d) 8
  38. 38.How many factors does 93 have? (a) 2 (b) 4 (c) 3 (d) 5
  39. 39.How many factors does 17 have? (a) 4 (b) 1 (c) 3 (d) 2
  40. 40.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2 × 5 × 7³

Answer key

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

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