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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 23 · 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 40 and 50? (a) 5 (b) 4 (c) 3 (d) 2
  2. 2.How many factors does 67 have? (a) 3 (b) 4 (c) 1 (d) 2
  3. 3.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 7 (d) 5
  4. 4.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 4 (d) 2
  5. 5.How many factors does 42 have? (a) 7 (b) 9 (c) 6 (d) 8
  6. 6.How many factors does 112 have? (a) 10 (b) 9 (c) 11 (d) 8
  7. 7.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁴ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2³ × 3 × 5
  8. 8.What is the smallest prime factor of 155? (a) 31 (b) 5 (c) 2 (d) 1
  9. 9.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 3 (d) 2
  10. 10.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 7 (d) 1
  11. 11.How many factors does 107 have? (a) 3 (b) 1 (c) 4 (d) 2
  12. 12.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 6 (d) 9
  13. 13.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 1 (d) 7
  14. 14.What is the smallest prime factor of 65? (a) 1 (b) 5 (c) 13 (d) 2
  15. 15.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
  16. 16.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 6 (d) 9
  17. 17.How many factors does 35 have? (a) 4 (b) 3 (c) 5 (d) 2
  18. 18.What is the smallest prime factor of 203? (a) 2 (b) 1 (c) 7 (d) 29
  19. 19.How many prime numbers are there between 50 and 80? (a) 6 (b) 7 (c) 8 (d) 9
  20. 20.How many factors does 73 have? (a) 3 (b) 1 (c) 2 (d) 4
  21. 21.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  22. 22.How many prime numbers are there between 10 and 40? (a) 10 (b) 9 (c) 7 (d) 8
  23. 23.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 1 (d) 3
  24. 24.What is the prime factorisation of 24? (a) 2² × 3 (b) 2³ × 3 (c) 2⁴ × 3 (d) 2 × 3³
  25. 25.What is the prime factorisation of 63? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
  26. 26.How many factors does 91 have? (a) 5 (b) 3 (c) 4 (d) 2
  27. 27.What is the smallest prime factor of 221? (a) 1 (b) 2 (c) 17 (d) 13
  28. 28.How many factors does 65 have? (a) 2 (b) 3 (c) 5 (d) 4
  29. 29.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  30. 30.How many factors does 19 have? (a) 4 (b) 1 (c) 2 (d) 3
  31. 31.How many factors does 61 have? (a) 1 (b) 4 (c) 3 (d) 2
  32. 32.What is the smallest prime factor of 55? (a) 11 (b) 2 (c) 5 (d) 1
  33. 33.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2³ × 7
  34. 34.How many prime numbers are there between 60 and 90? (a) 7 (b) 6 (c) 8 (d) 9
  35. 35.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 2 (d) 11
  36. 36.What is the smallest prime factor of 377? (a) 29 (b) 2 (c) 13 (d) 1
  37. 37.What is the smallest prime factor of 209? (a) 2 (b) 11 (c) 1 (d) 19
  38. 38.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  39. 39.How many factors does 40 have? (a) 7 (b) 9 (c) 6 (d) 8
  40. 40.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7

Answer key

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

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