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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 203 · 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 114 have? (a) 7 (b) 8 (c) 6 (d) 9
  2. 2.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 1 (d) 2
  3. 3.How many factors does 94 have? (a) 4 (b) 3 (c) 2 (d) 5
  4. 4.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 1 (d) 3
  5. 5.How many prime numbers are there between 30 and 60? (a) 9 (b) 8 (c) 7 (d) 6
  6. 6.How many factors does 26 have? (a) 2 (b) 4 (c) 5 (d) 3
  7. 7.What is the smallest prime factor of 145? (a) 29 (b) 1 (c) 5 (d) 2
  8. 8.How many factors does 14 have? (a) 2 (b) 5 (c) 3 (d) 4
  9. 9.What is the smallest prime factor of 203? (a) 1 (b) 2 (c) 7 (d) 29
  10. 10.What is the smallest prime factor of 209? (a) 2 (b) 1 (c) 11 (d) 19
  11. 11.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2⁴ × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  12. 12.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 2 (d) 7
  13. 13.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 4 (d) 1
  14. 14.What is the prime factorisation of 18? (a) 2 × 3² (b) 2² × 3 (c) 2 × 3³ (d) 2² × 3²
  15. 15.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 4 (d) 2
  16. 16.How many factors does 102 have? (a) 6 (b) 7 (c) 8 (d) 9
  17. 17.How many factors does 117 have? (a) 7 (b) 4 (c) 6 (d) 5
  18. 18.How many factors does 83 have? (a) 3 (b) 4 (c) 1 (d) 2
  19. 19.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
  20. 20.How many factors does 106 have? (a) 4 (b) 5 (c) 3 (d) 2
  21. 21.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 1 (d) 2
  22. 22.How many prime numbers are there between 20 and 40? (a) 6 (b) 4 (c) 3 (d) 5
  23. 23.What is the smallest prime factor of 69? (a) 23 (b) 1 (c) 3 (d) 2
  24. 24.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  25. 25.How many factors does 78 have? (a) 6 (b) 9 (c) 7 (d) 8
  26. 26.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  27. 27.How many factors does 56 have? (a) 6 (b) 7 (c) 9 (d) 8
  28. 28.How many factors does 84 have? (a) 10 (b) 13 (c) 12 (d) 11
  29. 29.How many factors does 63 have? (a) 6 (b) 5 (c) 7 (d) 4
  30. 30.What is the smallest prime factor of 35? (a) 1 (b) 7 (c) 2 (d) 5
  31. 31.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 6 (d) 7
  32. 32.How many prime numbers are there between 90 and 120? (a) 5 (b) 7 (c) 6 (d) 8
  33. 33.How many factors does 76 have? (a) 7 (b) 6 (c) 4 (d) 5
  34. 34.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  35. 35.How many factors does 85 have? (a) 5 (b) 2 (c) 4 (d) 3
  36. 36.What is the smallest prime factor of 57? (a) 1 (b) 19 (c) 3 (d) 2
  37. 37.How many factors does 34 have? (a) 3 (b) 5 (c) 2 (d) 4
  38. 38.How many factors does 112 have? (a) 8 (b) 11 (c) 10 (d) 9
  39. 39.What is the smallest prime factor of 161? (a) 7 (b) 23 (c) 2 (d) 1
  40. 40.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 6 (d) 7

Answer key

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

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