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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 47 · 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 253? (a) 2 (b) 11 (c) 1 (d) 23
  2. 2.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2³ × 3² × 5
  3. 3.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  4. 4.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  5. 5.What is the smallest prime factor of 133? (a) 19 (b) 1 (c) 2 (d) 7
  6. 6.How many factors does 44 have? (a) 7 (b) 6 (c) 4 (d) 5
  7. 7.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
  8. 8.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 7 (d) 6
  9. 9.How many factors does 38 have? (a) 5 (b) 3 (c) 4 (d) 2
  10. 10.What is the smallest prime factor of 209? (a) 19 (b) 1 (c) 2 (d) 11
  11. 11.How many factors does 25 have? (a) 2 (b) 1 (c) 3 (d) 4
  12. 12.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  13. 13.What is the prime factorisation of 12? (a) 2 × 3 (b) 2³ × 3 (c) 2² × 3 (d) 2 × 3²
  14. 14.What is the smallest prime factor of 85? (a) 2 (b) 17 (c) 5 (d) 1
  15. 15.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 2 (d) 3
  16. 16.How many factors does 28 have? (a) 7 (b) 5 (c) 6 (d) 4
  17. 17.How many factors does 101 have? (a) 1 (b) 2 (c) 4 (d) 3
  18. 18.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 3 (d) 11
  19. 19.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 7 (d) 6
  20. 20.How many factors does 116 have? (a) 4 (b) 6 (c) 5 (d) 7
  21. 21.How many prime numbers are there between 10 and 30? (a) 6 (b) 7 (c) 5 (d) 8
  22. 22.What is the smallest prime factor of 221? (a) 13 (b) 2 (c) 1 (d) 17
  23. 23.How many factors does 113 have? (a) 3 (b) 4 (c) 1 (d) 2
  24. 24.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 6 (d) 4
  25. 25.What is the smallest prime factor of 169? (a) 13 (b) 1 (c) 3 (d) 2
  26. 26.How many factors does 119 have? (a) 2 (b) 3 (c) 5 (d) 4
  27. 27.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5
  28. 28.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  29. 29.How many factors does 108 have? (a) 12 (b) 11 (c) 10 (d) 13
  30. 30.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  31. 31.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  32. 32.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7 (c) 2 × 7² (d) 2³ × 7
  33. 33.How many factors does 45 have? (a) 6 (b) 5 (c) 4 (d) 7
  34. 34.How many factors does 56 have? (a) 7 (b) 6 (c) 8 (d) 9
  35. 35.What is the smallest prime factor of 143? (a) 11 (b) 1 (c) 13 (d) 2
  36. 36.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2² × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
  37. 37.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 5 (d) 4
  38. 38.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 6 (d) 9
  39. 39.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
  40. 40.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 2 (d) 3

Answer key

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

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