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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 102 · 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 70 and 90? (a) 6 (b) 7 (c) 4 (d) 5
  2. 2.How many prime numbers are there between 10 and 30? (a) 5 (b) 7 (c) 8 (d) 6
  3. 3.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 3 (d) 2
  4. 4.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
  5. 5.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 5 (d) 1
  6. 6.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 7 (d) 9
  7. 7.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 10 (d) 9
  8. 8.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 5 (d) 6
  9. 9.How many factors does 96 have? (a) 13 (b) 11 (c) 10 (d) 12
  10. 10.How many factors does 94 have? (a) 2 (b) 4 (c) 5 (d) 3
  11. 11.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 8 (d) 9
  12. 12.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
  13. 13.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁵ × 7 (c) 2 × 7⁴ (d) 2⁴ × 7
  14. 14.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2⁴ × 3² (c) 2² × 3⁴ (d) 2³ × 3²
  15. 15.How many factors does 80 have? (a) 8 (b) 11 (c) 10 (d) 9
  16. 16.How many factors does 117 have? (a) 7 (b) 6 (c) 5 (d) 4
  17. 17.How many prime numbers are there between 40 and 50? (a) 2 (b) 3 (c) 4 (d) 5
  18. 18.How many factors does 105 have? (a) 6 (b) 8 (c) 7 (d) 9
  19. 19.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  20. 20.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 2 (d) 1
  21. 21.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 1 (d) 31
  22. 22.What is the smallest prime factor of 217? (a) 31 (b) 2 (c) 7 (d) 1
  23. 23.How many factors does 100 have? (a) 9 (b) 8 (c) 7 (d) 10
  24. 24.How many factors does 24 have? (a) 7 (b) 9 (c) 6 (d) 8
  25. 25.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 3 (d) 2
  26. 26.How many factors does 69 have? (a) 3 (b) 4 (c) 2 (d) 5
  27. 27.What is the smallest prime factor of 115? (a) 1 (b) 5 (c) 2 (d) 23
  28. 28.How many factors does 55 have? (a) 2 (b) 3 (c) 5 (d) 4
  29. 29.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
  30. 30.How many prime numbers are there between 80 and 110? (a) 7 (b) 9 (c) 6 (d) 8
  31. 31.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2⁴ × 5 × 7
  32. 32.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2 × 3 × 5
  33. 33.What is the prime factorisation of 12? (a) 2 × 3² (b) 2 × 3 (c) 2² × 3 (d) 2³ × 3
  34. 34.How many prime numbers are there between 50 and 80? (a) 8 (b) 7 (c) 6 (d) 9
  35. 35.How many prime numbers are there between 20 and 40? (a) 5 (b) 3 (c) 6 (d) 4
  36. 36.What is the prime factorisation of 21? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
  37. 37.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2 × 3 × 5³ (c) 2³ × 3 × 5 (d) 2⁴ × 3 × 5
  38. 38.How many prime numbers are there between 60 and 70? (a) 1 (b) 3 (c) 2 (d) 4
  39. 39.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 29 (d) 2
  40. 40.How many prime numbers are there between 90 and 120? (a) 5 (b) 8 (c) 7 (d) 6

Answer key

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

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