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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 132 · 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 prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  2. 2.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  3. 3.What is the smallest prime factor of 169? (a) 3 (b) 2 (c) 13 (d) 1
  4. 4.What is the smallest prime factor of 87? (a) 29 (b) 1 (c) 2 (d) 3
  5. 5.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
  6. 6.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 11 (d) 2
  7. 7.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  8. 8.What is the prime factorisation of 20? (a) 2 × 5² (b) 2³ × 5 (c) 2 × 5 (d) 2² × 5
  9. 9.How many factors does 106 have? (a) 4 (b) 5 (c) 2 (d) 3
  10. 10.What is the smallest prime factor of 33? (a) 2 (b) 3 (c) 11 (d) 1
  11. 11.How many factors does 87 have? (a) 2 (b) 5 (c) 4 (d) 3
  12. 12.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 7 (d) 2
  13. 13.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
  14. 14.How many factors does 29 have? (a) 1 (b) 3 (c) 4 (d) 2
  15. 15.How many prime numbers are there between 70 and 80? (a) 2 (b) 3 (c) 4 (d) 5
  16. 16.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 4 (d) 5
  17. 17.What is the prime factorisation of 63? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
  18. 18.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  19. 19.How many factors does 76 have? (a) 6 (b) 7 (c) 4 (d) 5
  20. 20.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 7 (d) 6
  21. 21.How many factors does 34 have? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.How many factors does 73 have? (a) 3 (b) 2 (c) 4 (d) 1
  23. 23.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 4 (d) 3
  24. 24.How many factors does 100 have? (a) 8 (b) 10 (c) 7 (d) 9
  25. 25.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 4 (d) 6
  26. 26.How many factors does 118 have? (a) 5 (b) 3 (c) 2 (d) 4
  27. 27.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2² × 7
  28. 28.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 2 (d) 5
  29. 29.How many factors does 65 have? (a) 5 (b) 3 (c) 2 (d) 4
  30. 30.How many factors does 12 have? (a) 7 (b) 6 (c) 5 (d) 4
  31. 31.How many factors does 39 have? (a) 2 (b) 4 (c) 3 (d) 5
  32. 32.How many factors does 64 have? (a) 7 (b) 6 (c) 5 (d) 8
  33. 33.How many factors does 93 have? (a) 5 (b) 2 (c) 4 (d) 3
  34. 34.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 7 (d) 1
  35. 35.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
  36. 36.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2 × 3² × 7
  37. 37.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  38. 38.How many factors does 55 have? (a) 3 (b) 2 (c) 4 (d) 5
  39. 39.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁵ × 3 × 7
  40. 40.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 1 (d) 2

Answer key

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

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