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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 154 · 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 smallest prime factor of 403? (a) 1 (b) 2 (c) 31 (d) 13
  2. 2.How many factors does 16 have? (a) 5 (b) 6 (c) 3 (d) 4
  3. 3.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 7 (d) 6
  4. 4.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  5. 5.How many factors does 74 have? (a) 4 (b) 5 (c) 3 (d) 2
  6. 6.How many factors does 78 have? (a) 6 (b) 7 (c) 8 (d) 9
  7. 7.How many factors does 59 have? (a) 3 (b) 1 (c) 4 (d) 2
  8. 8.What is the prime factorisation of 35? (a) 5 × 7² (b) 5² × 7 (c) 5 × 7 (d) 5³ × 7
  9. 9.What is the prime factorisation of 28? (a) 2 × 7 (b) 2² × 7 (c) 2 × 7² (d) 2³ × 7
  10. 10.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 1 (d) 2
  11. 11.How many factors does 30 have? (a) 7 (b) 9 (c) 8 (d) 6
  12. 12.What is the prime factorisation of 18? (a) 2² × 3² (b) 2² × 3 (c) 2 × 3³ (d) 2 × 3²
  13. 13.How many factors does 118 have? (a) 2 (b) 3 (c) 5 (d) 4
  14. 14.What is the smallest prime factor of 155? (a) 1 (b) 5 (c) 2 (d) 31
  15. 15.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  16. 16.What is the prime factorisation of 12? (a) 2 × 3 (b) 2³ × 3 (c) 2 × 3² (d) 2² × 3
  17. 17.How many prime numbers are there between 90 and 100? (a) 3 (b) 1 (c) 0 (d) 2
  18. 18.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2 × 5 × 7 (d) 2³ × 5 × 7
  19. 19.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 5 (d) 17
  20. 20.What is the smallest prime factor of 87? (a) 29 (b) 2 (c) 1 (d) 3
  21. 21.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 11 (d) 7
  22. 22.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
  23. 23.How many factors does 40 have? (a) 6 (b) 9 (c) 7 (d) 8
  24. 24.What is the smallest prime factor of 247? (a) 13 (b) 2 (c) 19 (d) 1
  25. 25.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7⁴
  26. 26.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
  27. 27.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5² (c) 2 × 5 (d) 2² × 5
  28. 28.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
  29. 29.How many factors does 26 have? (a) 3 (b) 2 (c) 5 (d) 4
  30. 30.How many factors does 71 have? (a) 4 (b) 2 (c) 1 (d) 3
  31. 31.How many factors does 60 have? (a) 11 (b) 10 (c) 12 (d) 13
  32. 32.How many factors does 36 have? (a) 7 (b) 10 (c) 8 (d) 9
  33. 33.What is the smallest prime factor of 65? (a) 13 (b) 5 (c) 1 (d) 2
  34. 34.What is the smallest prime factor of 57? (a) 3 (b) 2 (c) 19 (d) 1
  35. 35.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2
  36. 36.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  37. 37.How many factors does 96 have? (a) 12 (b) 13 (c) 11 (d) 10
  38. 38.What is the smallest prime factor of 49? (a) 1 (b) 2 (c) 3 (d) 7
  39. 39.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
  40. 40.What is the smallest prime factor of 143? (a) 2 (b) 11 (c) 13 (d) 1

Answer key

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

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