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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 57 · 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 20 and 30? (a) 2 (b) 1 (c) 3 (d) 4
  2. 2.How many factors does 108 have? (a) 12 (b) 13 (c) 10 (d) 11
  3. 3.How many factors does 63 have? (a) 4 (b) 6 (c) 7 (d) 5
  4. 4.How many factors does 29 have? (a) 2 (b) 3 (c) 1 (d) 4
  5. 5.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 3 (d) 1
  6. 6.What is the smallest prime factor of 377? (a) 13 (b) 1 (c) 29 (d) 2
  7. 7.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 6 (d) 7
  8. 8.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
  9. 9.How many factors does 71 have? (a) 2 (b) 1 (c) 4 (d) 3
  10. 10.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 1 (d) 5
  11. 11.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 23 (d) 7
  12. 12.How many factors does 58 have? (a) 5 (b) 2 (c) 3 (d) 4
  13. 13.How many factors does 118 have? (a) 2 (b) 3 (c) 4 (d) 5
  14. 14.How many prime numbers are there between 60 and 90? (a) 8 (b) 6 (c) 9 (d) 7
  15. 15.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7³ (d) 2⁴ × 7
  16. 16.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3 (c) 2 × 3² (d) 2² × 3²
  17. 17.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 1 (d) 3
  18. 18.What is the smallest prime factor of 203? (a) 29 (b) 1 (c) 7 (d) 2
  19. 19.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2 × 5⁴ (c) 2⁵ × 5 (d) 2⁴ × 5
  20. 20.What is the smallest prime factor of 35? (a) 7 (b) 1 (c) 2 (d) 5
  21. 21.How many factors does 67 have? (a) 1 (b) 3 (c) 4 (d) 2
  22. 22.How many factors does 95 have? (a) 5 (b) 4 (c) 3 (d) 2
  23. 23.How many factors does 117 have? (a) 7 (b) 4 (c) 6 (d) 5
  24. 24.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁵ × 3 × 7
  25. 25.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 6 (d) 8
  26. 26.How many factors does 52 have? (a) 6 (b) 4 (c) 5 (d) 7
  27. 27.How many factors does 59 have? (a) 1 (b) 2 (c) 4 (d) 3
  28. 28.How many factors does 43 have? (a) 2 (b) 4 (c) 3 (d) 1
  29. 29.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5 × 7² (c) 5² × 7 (d) 5 × 7
  30. 30.What is the smallest prime factor of 403? (a) 2 (b) 1 (c) 31 (d) 13
  31. 31.How many prime numbers are there between 90 and 100? (a) 3 (b) 1 (c) 2 (d) 0
  32. 32.How many factors does 16 have? (a) 6 (b) 5 (c) 3 (d) 4
  33. 33.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  34. 34.How many factors does 45 have? (a) 5 (b) 6 (c) 7 (d) 4
  35. 35.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3 × 7 (d) 3³ × 7
  36. 36.What is the smallest prime factor of 115? (a) 23 (b) 2 (c) 1 (d) 5
  37. 37.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2 × 3² × 5³
  38. 38.How many prime numbers are there between 90 and 120? (a) 6 (b) 7 (c) 5 (d) 8
  39. 39.How many factors does 110 have? (a) 9 (b) 7 (c) 8 (d) 6
  40. 40.How many factors does 57 have? (a) 2 (b) 3 (c) 5 (d) 4

Answer key

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

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