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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 17 · 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 40? (a) 10 (b) 8 (c) 7 (d) 9
  2. 2.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
  3. 3.How many factors does 28 have? (a) 5 (b) 7 (c) 6 (d) 4
  4. 4.What is the smallest prime factor of 65? (a) 5 (b) 2 (c) 1 (d) 13
  5. 5.How many prime numbers are there between 70 and 100? (a) 5 (b) 6 (c) 8 (d) 7
  6. 6.How many prime numbers are there between 70 and 90? (a) 4 (b) 6 (c) 5 (d) 7
  7. 7.How many factors does 75 have? (a) 7 (b) 6 (c) 5 (d) 4
  8. 8.How many factors does 15 have? (a) 4 (b) 5 (c) 2 (d) 3
  9. 9.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2² × 3 × 5 (c) 2 × 3 × 5 (d) 2³ × 3 × 5
  10. 10.How many factors does 65 have? (a) 3 (b) 4 (c) 2 (d) 5
  11. 11.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 3 (d) 2
  12. 12.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2⁴ × 5 (c) 2² × 5 (d) 2 × 5³
  13. 13.How many prime numbers are there between 90 and 110? (a) 7 (b) 6 (c) 4 (d) 5
  14. 14.What is the smallest prime factor of 35? (a) 2 (b) 1 (c) 5 (d) 7
  15. 15.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7 (c) 3 × 7² (d) 3² × 7
  16. 16.How many factors does 119 have? (a) 5 (b) 4 (c) 2 (d) 3
  17. 17.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  18. 18.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5³
  19. 19.How many factors does 66 have? (a) 6 (b) 9 (c) 7 (d) 8
  20. 20.How many factors does 120 have? (a) 16 (b) 17 (c) 15 (d) 14
  21. 21.How many factors does 67 have? (a) 4 (b) 1 (c) 3 (d) 2
  22. 22.How many factors does 86 have? (a) 4 (b) 2 (c) 5 (d) 3
  23. 23.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
  24. 24.How many factors does 106 have? (a) 3 (b) 5 (c) 4 (d) 2
  25. 25.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2² × 7
  26. 26.How many factors does 117 have? (a) 6 (b) 4 (c) 7 (d) 5
  27. 27.How many factors does 73 have? (a) 2 (b) 1 (c) 3 (d) 4
  28. 28.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3² (d) 2 × 3
  29. 29.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 6 (d) 8
  30. 30.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 2 (d) 3
  31. 31.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 5 (d) 6
  32. 32.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 5 (d) 6
  33. 33.How many factors does 27 have? (a) 3 (b) 5 (c) 2 (d) 4
  34. 34.What is the smallest prime factor of 319? (a) 1 (b) 11 (c) 29 (d) 2
  35. 35.What is the smallest prime factor of 187? (a) 11 (b) 2 (c) 1 (d) 17
  36. 36.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 2 (d) 4
  37. 37.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁵ × 3² (d) 2⁴ × 3²
  38. 38.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
  39. 39.How many factors does 52 have? (a) 4 (b) 5 (c) 7 (d) 6
  40. 40.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 6 (d) 9

Answer key

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

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