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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 128 · 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.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
  2. 2.What is the smallest prime factor of 341? (a) 2 (b) 31 (c) 11 (d) 1
  3. 3.How many factors does 44 have? (a) 7 (b) 4 (c) 6 (d) 5
  4. 4.How many factors does 83 have? (a) 3 (b) 4 (c) 1 (d) 2
  5. 5.How many factors does 27 have? (a) 3 (b) 2 (c) 4 (d) 5
  6. 6.How many factors does 50 have? (a) 4 (b) 7 (c) 6 (d) 5
  7. 7.How many factors does 13 have? (a) 3 (b) 2 (c) 1 (d) 4
  8. 8.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7² (c) 3² × 7 (d) 3 × 7
  9. 9.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
  10. 10.What is the smallest prime factor of 221? (a) 17 (b) 2 (c) 13 (d) 1
  11. 11.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 6 (d) 5
  12. 12.How many factors does 38 have? (a) 4 (b) 5 (c) 2 (d) 3
  13. 13.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 3 (d) 1
  14. 14.How many factors does 76 have? (a) 4 (b) 5 (c) 7 (d) 6
  15. 15.What is the smallest prime factor of 21? (a) 1 (b) 7 (c) 2 (d) 3
  16. 16.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3 × 7 (d) 3³ × 7
  17. 17.What is the smallest prime factor of 203? (a) 2 (b) 29 (c) 7 (d) 1
  18. 18.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  19. 19.How many factors does 70 have? (a) 7 (b) 9 (c) 6 (d) 8
  20. 20.How many prime numbers are there between 60 and 80? (a) 4 (b) 6 (c) 5 (d) 7
  21. 21.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 8 (d) 7
  22. 22.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 23 (d) 1
  23. 23.How many factors does 106 have? (a) 4 (b) 5 (c) 2 (d) 3
  24. 24.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  25. 25.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  26. 26.What is the smallest prime factor of 247? (a) 1 (b) 2 (c) 19 (d) 13
  27. 27.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 8 (d) 9
  28. 28.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 5 (d) 6
  29. 29.What is the smallest prime factor of 319? (a) 1 (b) 29 (c) 11 (d) 2
  30. 30.How many prime numbers are there between 30 and 60? (a) 9 (b) 7 (c) 6 (d) 8
  31. 31.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 4 (d) 5
  32. 32.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 7 (d) 4
  33. 33.How many factors does 57 have? (a) 4 (b) 2 (c) 5 (d) 3
  34. 34.How many factors does 82 have? (a) 3 (b) 2 (c) 4 (d) 5
  35. 35.How many factors does 14 have? (a) 4 (b) 2 (c) 5 (d) 3
  36. 36.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
  37. 37.How many factors does 47 have? (a) 3 (b) 4 (c) 1 (d) 2
  38. 38.What is the smallest prime factor of 65? (a) 13 (b) 2 (c) 1 (d) 5
  39. 39.How many factors does 21 have? (a) 2 (b) 3 (c) 4 (d) 5
  40. 40.How many factors does 45 have? (a) 7 (b) 5 (c) 6 (d) 4

Answer key

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

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