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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 62 · 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 99 have? (a) 7 (b) 4 (c) 6 (d) 5
  2. 2.How many factors does 73 have? (a) 4 (b) 1 (c) 2 (d) 3
  3. 3.How many factors does 66 have? (a) 7 (b) 6 (c) 9 (d) 8
  4. 4.How many factors does 32 have? (a) 5 (b) 4 (c) 6 (d) 7
  5. 5.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2⁵ × 7
  6. 6.How many factors does 116 have? (a) 4 (b) 7 (c) 5 (d) 6
  7. 7.What is the prime factorisation of 21? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
  8. 8.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 3 (d) 2
  9. 9.How many factors does 104 have? (a) 6 (b) 8 (c) 9 (d) 7
  10. 10.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7 (d) 5 × 7²
  11. 11.How many factors does 50 have? (a) 6 (b) 4 (c) 7 (d) 5
  12. 12.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 3 (d) 4
  13. 13.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2⁴ × 7 (d) 2 × 7³
  14. 14.How many factors does 87 have? (a) 5 (b) 2 (c) 4 (d) 3
  15. 15.How many factors does 78 have? (a) 7 (b) 9 (c) 6 (d) 8
  16. 16.How many factors does 70 have? (a) 9 (b) 6 (c) 8 (d) 7
  17. 17.What is the smallest prime factor of 55? (a) 2 (b) 1 (c) 5 (d) 11
  18. 18.How many factors does 115 have? (a) 4 (b) 3 (c) 5 (d) 2
  19. 19.What is the smallest prime factor of 161? (a) 7 (b) 1 (c) 2 (d) 23
  20. 20.How many factors does 20 have? (a) 7 (b) 6 (c) 4 (d) 5
  21. 21.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  22. 22.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  23. 23.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3³ × 5 (d) 3 × 5²
  24. 24.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  25. 25.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 6 (d) 7
  26. 26.How many factors does 56 have? (a) 8 (b) 9 (c) 6 (d) 7
  27. 27.How many factors does 77 have? (a) 3 (b) 2 (c) 5 (d) 4
  28. 28.What is the smallest prime factor of 187? (a) 1 (b) 2 (c) 11 (d) 17
  29. 29.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 4 (d) 5
  30. 30.How many factors does 65 have? (a) 2 (b) 4 (c) 5 (d) 3
  31. 31.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5 (c) 3³ × 5 (d) 3 × 5²
  32. 32.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 3 (d) 1
  33. 33.How many factors does 33 have? (a) 4 (b) 2 (c) 3 (d) 5
  34. 34.How many factors does 74 have? (a) 2 (b) 3 (c) 5 (d) 4
  35. 35.What is the smallest prime factor of 85? (a) 2 (b) 5 (c) 17 (d) 1
  36. 36.How many factors does 43 have? (a) 3 (b) 1 (c) 2 (d) 4
  37. 37.How many factors does 113 have? (a) 3 (b) 4 (c) 2 (d) 1
  38. 38.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
  39. 39.How many factors does 84 have? (a) 10 (b) 11 (c) 13 (d) 12
  40. 40.How many factors does 17 have? (a) 3 (b) 1 (c) 4 (d) 2

Answer key

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

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