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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 133 · 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 85? (a) 1 (b) 5 (c) 2 (d) 17
  2. 2.How many factors does 41 have? (a) 1 (b) 2 (c) 4 (d) 3
  3. 3.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2 × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  4. 4.How many factors does 44 have? (a) 7 (b) 5 (c) 4 (d) 6
  5. 5.How many factors does 12 have? (a) 6 (b) 4 (c) 7 (d) 5
  6. 6.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 4 (d) 2
  7. 7.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 9 (d) 8
  8. 8.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
  9. 9.How many prime numbers are there between 70 and 80? (a) 2 (b) 4 (c) 5 (d) 3
  10. 10.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2² × 5 (c) 2 × 5 (d) 2 × 5²
  11. 11.How many factors does 28 have? (a) 7 (b) 5 (c) 4 (d) 6
  12. 12.What is the prime factorisation of 45? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
  13. 13.What is the smallest prime factor of 203? (a) 1 (b) 7 (c) 29 (d) 2
  14. 14.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 2 (d) 11
  15. 15.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 5 (d) 3
  16. 16.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2⁴ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2³ × 5 × 7
  17. 17.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 9 (d) 7
  18. 18.How many factors does 49 have? (a) 1 (b) 2 (c) 3 (d) 4
  19. 19.How many prime numbers are there between 60 and 70? (a) 4 (b) 3 (c) 1 (d) 2
  20. 20.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2³ × 3² × 5 (d) 2 × 3² × 5
  21. 21.How many factors does 54 have? (a) 8 (b) 6 (c) 7 (d) 9
  22. 22.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 5 (d) 31
  23. 23.What is the smallest prime factor of 87? (a) 1 (b) 3 (c) 2 (d) 29
  24. 24.How many factors does 58 have? (a) 3 (b) 5 (c) 4 (d) 2
  25. 25.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 7 (d) 2
  26. 26.How many factors does 76 have? (a) 6 (b) 7 (c) 5 (d) 4
  27. 27.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  28. 28.What is the smallest prime factor of 119? (a) 1 (b) 7 (c) 17 (d) 2
  29. 29.What is the smallest prime factor of 115? (a) 1 (b) 23 (c) 2 (d) 5
  30. 30.How many factors does 45 have? (a) 4 (b) 5 (c) 7 (d) 6
  31. 31.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2³ × 7
  32. 32.What is the smallest prime factor of 209? (a) 11 (b) 1 (c) 19 (d) 2
  33. 33.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 1 (d) 2
  34. 34.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  35. 35.What is the smallest prime factor of 65? (a) 5 (b) 13 (c) 1 (d) 2
  36. 36.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 7 (d) 5
  37. 37.How many factors does 97 have? (a) 2 (b) 3 (c) 4 (d) 1
  38. 38.How many factors does 115 have? (a) 5 (b) 4 (c) 3 (d) 2
  39. 39.What is the smallest prime factor of 121? (a) 3 (b) 11 (c) 1 (d) 2
  40. 40.How many prime numbers are there between 30 and 50? (a) 6 (b) 5 (c) 4 (d) 7

Answer key

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

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