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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 205 · 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 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  2. 2.How many factors does 94 have? (a) 2 (b) 4 (c) 3 (d) 5
  3. 3.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5³ (d) 2³ × 3 × 5
  4. 4.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 4 (d) 2
  5. 5.How many factors does 108 have? (a) 10 (b) 11 (c) 12 (d) 13
  6. 6.How many prime numbers are there between 80 and 110? (a) 6 (b) 7 (c) 8 (d) 9
  7. 7.How many factors does 42 have? (a) 9 (b) 6 (c) 7 (d) 8
  8. 8.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 1 (d) 11
  9. 9.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2³ × 3
  10. 10.How many factors does 76 have? (a) 4 (b) 6 (c) 7 (d) 5
  11. 11.How many factors does 60 have? (a) 12 (b) 10 (c) 11 (d) 13
  12. 12.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2⁵ × 5 × 7
  13. 13.How many factors does 90 have? (a) 11 (b) 13 (c) 12 (d) 10
  14. 14.What is the smallest prime factor of 39? (a) 2 (b) 13 (c) 1 (d) 3
  15. 15.How many factors does 82 have? (a) 5 (b) 2 (c) 3 (d) 4
  16. 16.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 5 (d) 6
  17. 17.How many factors does 63 have? (a) 7 (b) 5 (c) 4 (d) 6
  18. 18.How many prime numbers are there between 50 and 80? (a) 7 (b) 8 (c) 9 (d) 6
  19. 19.How many factors does 18 have? (a) 7 (b) 6 (c) 4 (d) 5
  20. 20.How many factors does 116 have? (a) 5 (b) 4 (c) 7 (d) 6
  21. 21.How many factors does 68 have? (a) 4 (b) 5 (c) 7 (d) 6
  22. 22.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
  23. 23.How many factors does 58 have? (a) 5 (b) 2 (c) 3 (d) 4
  24. 24.How many factors does 54 have? (a) 9 (b) 6 (c) 8 (d) 7
  25. 25.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2⁴ × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  26. 26.How many factors does 95 have? (a) 4 (b) 5 (c) 3 (d) 2
  27. 27.How many prime numbers are there between 40 and 70? (a) 7 (b) 8 (c) 9 (d) 6
  28. 28.How many factors does 28 have? (a) 4 (b) 5 (c) 6 (d) 7
  29. 29.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  30. 30.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 5 (d) 4
  31. 31.How many prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 9 (d) 7
  32. 32.How many prime numbers are there between 70 and 80? (a) 2 (b) 3 (c) 5 (d) 4
  33. 33.How many factors does 111 have? (a) 3 (b) 2 (c) 5 (d) 4
  34. 34.How many factors does 45 have? (a) 6 (b) 5 (c) 4 (d) 7
  35. 35.What is the smallest prime factor of 121? (a) 2 (b) 3 (c) 11 (d) 1
  36. 36.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 4 (d) 2
  37. 37.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 8 (d) 5
  38. 38.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 1 (d) 4
  39. 39.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
  40. 40.How many factors does 103 have? (a) 3 (b) 4 (c) 2 (d) 1

Answer key

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

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