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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 198 · 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 10 and 30? (a) 8 (b) 5 (c) 7 (d) 6
  2. 2.How many factors does 13 have? (a) 4 (b) 1 (c) 3 (d) 2
  3. 3.How many factors does 97 have? (a) 4 (b) 1 (c) 2 (d) 3
  4. 4.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  5. 5.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2² × 3⁴ (c) 2⁵ × 3² (d) 2⁴ × 3²
  6. 6.How many prime numbers are there between 80 and 100? (a) 4 (b) 5 (c) 2 (d) 3
  7. 7.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
  8. 8.What is the smallest prime factor of 403? (a) 2 (b) 1 (c) 31 (d) 13
  9. 9.What is the smallest prime factor of 85? (a) 17 (b) 2 (c) 1 (d) 5
  10. 10.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 9 (d) 6
  11. 11.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2³ × 3² (c) 2² × 3² (d) 2⁴ × 3²
  12. 12.What is the smallest prime factor of 203? (a) 7 (b) 2 (c) 29 (d) 1
  13. 13.How many factors does 108 have? (a) 13 (b) 12 (c) 10 (d) 11
  14. 14.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 4 (d) 6
  15. 15.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
  16. 16.What is the smallest prime factor of 39? (a) 1 (b) 13 (c) 3 (d) 2
  17. 17.How many factors does 67 have? (a) 3 (b) 1 (c) 2 (d) 4
  18. 18.How many factors does 39 have? (a) 5 (b) 3 (c) 4 (d) 2
  19. 19.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 8 (d) 9
  20. 20.How many factors does 18 have? (a) 5 (b) 4 (c) 6 (d) 7
  21. 21.How many factors does 76 have? (a) 7 (b) 5 (c) 4 (d) 6
  22. 22.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 7 (d) 5
  23. 23.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  24. 24.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3 × 7
  25. 25.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
  26. 26.What is the prime factorisation of 12? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3 (d) 2 × 3²
  27. 27.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7³ (d) 2³ × 3² × 7
  28. 28.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁵ × 3 (d) 2⁴ × 3
  29. 29.How many factors does 62 have? (a) 5 (b) 3 (c) 4 (d) 2
  30. 30.What is the smallest prime factor of 93? (a) 3 (b) 31 (c) 2 (d) 1
  31. 31.How many factors does 95 have? (a) 5 (b) 3 (c) 2 (d) 4
  32. 32.How many factors does 86 have? (a) 2 (b) 3 (c) 4 (d) 5
  33. 33.What is the prime factorisation of 20? (a) 2 × 5² (b) 2³ × 5 (c) 2 × 5 (d) 2² × 5
  34. 34.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 9 (d) 7
  35. 35.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 2 (d) 4
  36. 36.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  37. 37.What is the smallest prime factor of 65? (a) 13 (b) 2 (c) 1 (d) 5
  38. 38.How many factors does 102 have? (a) 8 (b) 9 (c) 7 (d) 6
  39. 39.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 7 (d) 6
  40. 40.What is the smallest prime factor of 161? (a) 23 (b) 7 (c) 1 (d) 2

Answer key

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

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