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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 81 · 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 factors does 17 have? (a) 4 (b) 3 (c) 1 (d) 2
  2. 2.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 5 (d) 3
  3. 3.How many factors does 16 have? (a) 3 (b) 6 (c) 5 (d) 4
  4. 4.How many factors does 25 have? (a) 1 (b) 3 (c) 2 (d) 4
  5. 5.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  6. 6.How many factors does 66 have? (a) 9 (b) 7 (c) 6 (d) 8
  7. 7.What is the prime factorisation of 15? (a) 3 × 5² (b) 3³ × 5 (c) 3 × 5 (d) 3² × 5
  8. 8.How many factors does 77 have? (a) 2 (b) 3 (c) 4 (d) 5
  9. 9.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
  10. 10.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 9 (d) 6
  11. 11.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 2 (d) 1
  12. 12.How many factors does 24 have? (a) 9 (b) 8 (c) 7 (d) 6
  13. 13.How many factors does 74 have? (a) 2 (b) 4 (c) 3 (d) 5
  14. 14.How many factors does 22 have? (a) 3 (b) 5 (c) 2 (d) 4
  15. 15.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 6 (d) 3
  16. 16.What is the smallest prime factor of 33? (a) 11 (b) 3 (c) 1 (d) 2
  17. 17.How many factors does 29 have? (a) 4 (b) 3 (c) 2 (d) 1
  18. 18.How many factors does 103 have? (a) 2 (b) 3 (c) 1 (d) 4
  19. 19.How many factors does 68 have? (a) 4 (b) 6 (c) 5 (d) 7
  20. 20.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 5 (d) 3
  21. 21.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 13 (d) 11
  22. 22.How many factors does 61 have? (a) 3 (b) 4 (c) 1 (d) 2
  23. 23.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 3 (d) 1
  24. 24.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7³
  25. 25.What is the prime factorisation of 12? (a) 2² × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2 × 3
  26. 26.How many factors does 115 have? (a) 3 (b) 2 (c) 5 (d) 4
  27. 27.How many factors does 45 have? (a) 4 (b) 5 (c) 6 (d) 7
  28. 28.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
  29. 29.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
  30. 30.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 4 (d) 5
  31. 31.How many factors does 93 have? (a) 2 (b) 3 (c) 5 (d) 4
  32. 32.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 2 (d) 13
  33. 33.How many factors does 85 have? (a) 2 (b) 5 (c) 4 (d) 3
  34. 34.How many prime numbers are there between 70 and 80? (a) 5 (b) 4 (c) 2 (d) 3
  35. 35.How many prime numbers are there between 40 and 70? (a) 8 (b) 7 (c) 6 (d) 9
  36. 36.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2 × 3 × 5⁴
  37. 37.How many factors does 26 have? (a) 2 (b) 5 (c) 3 (d) 4
  38. 38.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 4 (d) 6
  39. 39.What is the smallest prime factor of 247? (a) 1 (b) 2 (c) 13 (d) 19
  40. 40.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁵ × 3² (c) 2³ × 3² (d) 2⁴ × 3²

Answer key

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

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