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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 49 · 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 50 and 70? (a) 6 (b) 4 (c) 3 (d) 5
  2. 2.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
  3. 3.What is the smallest prime factor of 133? (a) 19 (b) 2 (c) 1 (d) 7
  4. 4.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  5. 5.What is the prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5²
  6. 6.How many factors does 60 have? (a) 11 (b) 10 (c) 13 (d) 12
  7. 7.What is the smallest prime factor of 35? (a) 2 (b) 5 (c) 7 (d) 1
  8. 8.What is the smallest prime factor of 377? (a) 2 (b) 1 (c) 29 (d) 13
  9. 9.How many prime numbers are there between 80 and 90? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 7 (d) 6
  11. 11.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 4 (d) 3
  12. 12.What is the smallest prime factor of 55? (a) 2 (b) 11 (c) 5 (d) 1
  13. 13.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5³ (d) 2⁴ × 3² × 5
  14. 14.How many factors does 21 have? (a) 3 (b) 5 (c) 2 (d) 4
  15. 15.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 4 (d) 1
  16. 16.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 29 (d) 3
  17. 17.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2 × 3³ (c) 2² × 3 (d) 2⁴ × 3
  18. 18.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
  19. 19.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7³
  20. 20.How many factors does 103 have? (a) 2 (b) 3 (c) 1 (d) 4
  21. 21.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 7 (d) 10
  22. 22.How many prime numbers are there between 70 and 100? (a) 5 (b) 6 (c) 7 (d) 8
  23. 23.How many factors does 53 have? (a) 4 (b) 1 (c) 3 (d) 2
  24. 24.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  25. 25.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5
  26. 26.How many factors does 56 have? (a) 7 (b) 9 (c) 6 (d) 8
  27. 27.How many prime numbers are there between 30 and 60? (a) 6 (b) 9 (c) 7 (d) 8
  28. 28.How many factors does 29 have? (a) 3 (b) 4 (c) 2 (d) 1
  29. 29.How many factors does 104 have? (a) 7 (b) 9 (c) 6 (d) 8
  30. 30.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  31. 31.How many factors does 26 have? (a) 4 (b) 3 (c) 5 (d) 2
  32. 32.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
  33. 33.How many factors does 22 have? (a) 5 (b) 4 (c) 3 (d) 2
  34. 34.How many factors does 87 have? (a) 5 (b) 4 (c) 3 (d) 2
  35. 35.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 6 (d) 8
  36. 36.How many factors does 41 have? (a) 4 (b) 3 (c) 1 (d) 2
  37. 37.How many factors does 52 have? (a) 4 (b) 5 (c) 7 (d) 6
  38. 38.What is the smallest prime factor of 49? (a) 3 (b) 2 (c) 7 (d) 1
  39. 39.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 3 (d) 11
  40. 40.How many factors does 120 have? (a) 15 (b) 14 (c) 17 (d) 16

Answer key

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

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