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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 54 · 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 48 have? (a) 11 (b) 8 (c) 9 (d) 10
  2. 2.How many factors does 60 have? (a) 13 (b) 12 (c) 10 (d) 11
  3. 3.How many prime numbers are there between 90 and 110? (a) 7 (b) 4 (c) 6 (d) 5
  4. 4.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 5 (d) 6
  5. 5.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2² × 7 (d) 2³ × 7
  6. 6.What is the smallest prime factor of 119? (a) 1 (b) 17 (c) 2 (d) 7
  7. 7.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  8. 8.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5 × 7
  9. 9.How many factors does 18 have? (a) 6 (b) 5 (c) 4 (d) 7
  10. 10.How many prime numbers are there between 30 and 50? (a) 5 (b) 4 (c) 7 (d) 6
  11. 11.What is the smallest prime factor of 133? (a) 1 (b) 2 (c) 19 (d) 7
  12. 12.How many factors does 14 have? (a) 4 (b) 5 (c) 2 (d) 3
  13. 13.How many factors does 109 have? (a) 1 (b) 4 (c) 3 (d) 2
  14. 14.How many prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 9 (d) 7
  15. 15.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 3 (d) 6
  16. 16.How many factors does 34 have? (a) 3 (b) 5 (c) 4 (d) 2
  17. 17.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  18. 18.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  19. 19.What is the prime factorisation of 36? (a) 2² × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2 × 3²
  20. 20.What is the smallest prime factor of 247? (a) 1 (b) 19 (c) 13 (d) 2
  21. 21.How many factors does 37 have? (a) 1 (b) 4 (c) 3 (d) 2
  22. 22.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 1 (d) 7
  23. 23.What is the smallest prime factor of 403? (a) 1 (b) 2 (c) 31 (d) 13
  24. 24.What is the smallest prime factor of 209? (a) 1 (b) 19 (c) 11 (d) 2
  25. 25.How many factors does 33 have? (a) 4 (b) 2 (c) 5 (d) 3
  26. 26.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 1 (d) 3
  27. 27.What is the prime factorisation of 12? (a) 2 × 3² (b) 2³ × 3 (c) 2² × 3 (d) 2 × 3
  28. 28.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2⁴ × 5 (d) 2 × 5⁴
  29. 29.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  30. 30.How many factors does 54 have? (a) 6 (b) 7 (c) 9 (d) 8
  31. 31.How many factors does 98 have? (a) 5 (b) 4 (c) 7 (d) 6
  32. 32.How many factors does 26 have? (a) 2 (b) 5 (c) 3 (d) 4
  33. 33.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  34. 34.How many factors does 70 have? (a) 8 (b) 7 (c) 9 (d) 6
  35. 35.How many factors does 82 have? (a) 4 (b) 5 (c) 3 (d) 2
  36. 36.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 2 (d) 1
  37. 37.How many factors does 12 have? (a) 4 (b) 7 (c) 5 (d) 6
  38. 38.How many factors does 45 have? (a) 5 (b) 4 (c) 7 (d) 6
  39. 39.What is the smallest prime factor of 203? (a) 2 (b) 29 (c) 7 (d) 1
  40. 40.What is the smallest prime factor of 221? (a) 13 (b) 2 (c) 17 (d) 1

Answer key

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

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