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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 156 · 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 57? (a) 1 (b) 19 (c) 2 (d) 3
  2. 2.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 1 (d) 7
  3. 3.What is the smallest prime factor of 377? (a) 2 (b) 13 (c) 29 (d) 1
  4. 4.How many prime numbers are there between 90 and 100? (a) 3 (b) 0 (c) 2 (d) 1
  5. 5.How many factors does 47 have? (a) 2 (b) 3 (c) 1 (d) 4
  6. 6.What is the prime factorisation of 12? (a) 2 × 3 (b) 2³ × 3 (c) 2² × 3 (d) 2 × 3²
  7. 7.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2² × 3⁴ (c) 2⁵ × 3² (d) 2³ × 3²
  8. 8.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 3 (d) 1
  9. 9.How many factors does 41 have? (a) 2 (b) 3 (c) 4 (d) 1
  10. 10.What is the prime factorisation of 18? (a) 2 × 3² (b) 2² × 3² (c) 2² × 3 (d) 2 × 3³
  11. 11.How many factors does 76 have? (a) 7 (b) 6 (c) 5 (d) 4
  12. 12.How many factors does 73 have? (a) 2 (b) 4 (c) 3 (d) 1
  13. 13.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
  14. 14.What is the smallest prime factor of 169? (a) 1 (b) 3 (c) 2 (d) 13
  15. 15.How many factors does 40 have? (a) 6 (b) 8 (c) 7 (d) 9
  16. 16.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2⁴ × 3 (c) 2² × 3 (d) 2³ × 3
  17. 17.How many factors does 84 have? (a) 13 (b) 11 (c) 10 (d) 12
  18. 18.How many factors does 34 have? (a) 3 (b) 4 (c) 2 (d) 5
  19. 19.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
  20. 20.What is the smallest prime factor of 253? (a) 23 (b) 2 (c) 1 (d) 11
  21. 21.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7
  22. 22.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  23. 23.How many factors does 96 have? (a) 11 (b) 10 (c) 13 (d) 12
  24. 24.What is the smallest prime factor of 161? (a) 1 (b) 23 (c) 2 (d) 7
  25. 25.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 6 (d) 8
  26. 26.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
  27. 27.How many factors does 31 have? (a) 3 (b) 2 (c) 4 (d) 1
  28. 28.What is the prime factorisation of 14? (a) 2 × 7² (b) 2² × 7 (c) 2 × 7 (d) 2³ × 7
  29. 29.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2 × 5
  30. 30.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 7 (d) 6
  31. 31.How many factors does 91 have? (a) 5 (b) 3 (c) 2 (d) 4
  32. 32.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 7 (d) 6
  33. 33.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2 × 3² × 5³ (c) 2² × 3² × 5 (d) 2³ × 3² × 5
  34. 34.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7²
  35. 35.How many factors does 87 have? (a) 3 (b) 4 (c) 2 (d) 5
  36. 36.How many factors does 86 have? (a) 4 (b) 2 (c) 3 (d) 5
  37. 37.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
  38. 38.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
  39. 39.How many factors does 69 have? (a) 2 (b) 4 (c) 3 (d) 5
  40. 40.How many factors does 118 have? (a) 2 (b) 5 (c) 3 (d) 4

Answer key

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

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