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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 130 · 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 112 have? (a) 11 (b) 10 (c) 9 (d) 8
  2. 2.How many factors does 47 have? (a) 4 (b) 3 (c) 2 (d) 1
  3. 3.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 3 (d) 1
  4. 4.How many factors does 55 have? (a) 5 (b) 2 (c) 4 (d) 3
  5. 5.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 6 (d) 4
  6. 6.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 3 (d) 7
  7. 7.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 2 (d) 7
  8. 8.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 5 (d) 4
  9. 9.How many factors does 16 have? (a) 5 (b) 6 (c) 3 (d) 4
  10. 10.How many factors does 100 have? (a) 8 (b) 10 (c) 9 (d) 7
  11. 11.How many factors does 29 have? (a) 4 (b) 1 (c) 2 (d) 3
  12. 12.What is the smallest prime factor of 253? (a) 1 (b) 2 (c) 23 (d) 11
  13. 13.What is the smallest prime factor of 203? (a) 2 (b) 1 (c) 7 (d) 29
  14. 14.What is the prime factorisation of 12? (a) 2 × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2² × 3
  15. 15.How many factors does 86 have? (a) 3 (b) 2 (c) 4 (d) 5
  16. 16.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2⁵ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2³ × 5 × 7
  17. 17.What is the smallest prime factor of 209? (a) 1 (b) 19 (c) 11 (d) 2
  18. 18.What is the smallest prime factor of 143? (a) 11 (b) 2 (c) 1 (d) 13
  19. 19.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 1 (d) 5
  20. 20.How many factors does 89 have? (a) 3 (b) 1 (c) 2 (d) 4
  21. 21.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 6 (d) 7
  22. 22.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 2 (d) 0
  23. 23.How many factors does 35 have? (a) 4 (b) 3 (c) 2 (d) 5
  24. 24.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2⁴ × 3 (c) 2² × 3 (d) 2³ × 3
  25. 25.How many prime numbers are there between 10 and 40? (a) 8 (b) 10 (c) 7 (d) 9
  26. 26.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 3 (d) 4
  27. 27.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
  28. 28.How many factors does 12 have? (a) 7 (b) 6 (c) 5 (d) 4
  29. 29.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5⁴
  30. 30.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 3 (d) 4
  31. 31.How many factors does 105 have? (a) 8 (b) 9 (c) 7 (d) 6
  32. 32.What is the smallest prime factor of 161? (a) 2 (b) 7 (c) 1 (d) 23
  33. 33.How many factors does 53 have? (a) 1 (b) 4 (c) 2 (d) 3
  34. 34.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
  35. 35.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2² × 5 (c) 2³ × 5 (d) 2⁴ × 5
  36. 36.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2² × 5 × 7
  37. 37.How many factors does 75 have? (a) 7 (b) 4 (c) 5 (d) 6
  38. 38.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 11 (d) 1
  39. 39.What is the smallest prime factor of 133? (a) 1 (b) 2 (c) 19 (d) 7
  40. 40.What is the prime factorisation of 45? (a) 3 × 5 (b) 3 × 5² (c) 3² × 5 (d) 3³ × 5

Answer key

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

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