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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 194 · 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 107 have? (a) 4 (b) 1 (c) 2 (d) 3
  2. 2.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 8 (d) 9
  3. 3.How many factors does 70 have? (a) 8 (b) 9 (c) 6 (d) 7
  4. 4.How many factors does 95 have? (a) 5 (b) 3 (c) 2 (d) 4
  5. 5.What is the smallest prime factor of 51? (a) 17 (b) 3 (c) 1 (d) 2
  6. 6.How many factors does 22 have? (a) 3 (b) 4 (c) 5 (d) 2
  7. 7.How many factors does 77 have? (a) 4 (b) 5 (c) 2 (d) 3
  8. 8.How many factors does 112 have? (a) 9 (b) 8 (c) 10 (d) 11
  9. 9.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  10. 10.How many factors does 85 have? (a) 5 (b) 4 (c) 3 (d) 2
  11. 11.What is the smallest prime factor of 187? (a) 11 (b) 2 (c) 1 (d) 17
  12. 12.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2 × 3 × 7² (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  13. 13.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
  14. 14.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2³ × 7 (c) 2⁵ × 7 (d) 2⁴ × 7
  15. 15.How many factors does 29 have? (a) 3 (b) 2 (c) 4 (d) 1
  16. 16.What is the smallest prime factor of 65? (a) 5 (b) 2 (c) 13 (d) 1
  17. 17.How many factors does 18 have? (a) 6 (b) 7 (c) 5 (d) 4
  18. 18.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 6 (d) 4
  19. 19.How many factors does 114 have? (a) 8 (b) 7 (c) 6 (d) 9
  20. 20.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2 × 3² × 7³ (c) 2⁴ × 3² × 7 (d) 2² × 3² × 7
  21. 21.How many factors does 83 have? (a) 3 (b) 2 (c) 1 (d) 4
  22. 22.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 0 (d) 1
  23. 23.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 4 (d) 6
  24. 24.How many factors does 57 have? (a) 2 (b) 3 (c) 4 (d) 5
  25. 25.How many prime numbers are there between 10 and 30? (a) 6 (b) 7 (c) 8 (d) 5
  26. 26.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2² × 3² (c) 2³ × 3² (d) 2 × 3²
  27. 27.How many factors does 23 have? (a) 1 (b) 2 (c) 4 (d) 3
  28. 28.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13
  29. 29.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 4 (d) 5
  30. 30.How many factors does 89 have? (a) 1 (b) 2 (c) 4 (d) 3
  31. 31.How many factors does 106 have? (a) 2 (b) 3 (c) 5 (d) 4
  32. 32.What is the smallest prime factor of 39? (a) 2 (b) 3 (c) 13 (d) 1
  33. 33.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁵ × 3 (d) 2⁴ × 3
  34. 34.How many factors does 91 have? (a) 3 (b) 5 (c) 2 (d) 4
  35. 35.What is the smallest prime factor of 203? (a) 1 (b) 7 (c) 29 (d) 2
  36. 36.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
  37. 37.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
  38. 38.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  39. 39.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2⁴ × 3²
  40. 40.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3³ (c) 2 × 3² (d) 2² × 3²

Answer key

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

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