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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 15 · 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.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  2. 2.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  3. 3.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 1 (d) 7
  4. 4.How many factors does 42 have? (a) 8 (b) 9 (c) 7 (d) 6
  5. 5.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2³ × 7
  6. 6.How many factors does 94 have? (a) 5 (b) 4 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 20 and 30? (a) 2 (b) 3 (c) 4 (d) 1
  8. 8.How many factors does 89 have? (a) 1 (b) 4 (c) 3 (d) 2
  9. 9.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁵ × 3 × 7 (d) 2 × 3 × 7⁴
  10. 10.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
  11. 11.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  12. 12.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  13. 13.How many factors does 90 have? (a) 11 (b) 10 (c) 12 (d) 13
  14. 14.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2
  15. 15.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
  16. 16.What is the prime factorisation of 63? (a) 3² × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3 × 7
  17. 17.How many prime numbers are there between 30 and 40? (a) 1 (b) 2 (c) 4 (d) 3
  18. 18.How many factors does 67 have? (a) 1 (b) 2 (c) 4 (d) 3
  19. 19.How many factors does 80 have? (a) 11 (b) 9 (c) 8 (d) 10
  20. 20.How many factors does 105 have? (a) 9 (b) 7 (c) 6 (d) 8
  21. 21.What is the prime factorisation of 12? (a) 2 × 3² (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3
  22. 22.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 11 (d) 3
  23. 23.What is the smallest prime factor of 217? (a) 31 (b) 7 (c) 2 (d) 1
  24. 24.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  25. 25.What is the prime factorisation of 28? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
  26. 26.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4
  27. 27.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 5 (d) 1
  28. 28.How many factors does 12 have? (a) 4 (b) 7 (c) 6 (d) 5
  29. 29.How many factors does 109 have? (a) 4 (b) 1 (c) 2 (d) 3
  30. 30.How many factors does 117 have? (a) 7 (b) 4 (c) 6 (d) 5
  31. 31.What is the smallest prime factor of 93? (a) 31 (b) 1 (c) 3 (d) 2
  32. 32.How many factors does 92 have? (a) 4 (b) 6 (c) 7 (d) 5
  33. 33.What is the smallest prime factor of 85? (a) 5 (b) 1 (c) 2 (d) 17
  34. 34.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5
  35. 35.How many factors does 63 have? (a) 7 (b) 6 (c) 4 (d) 5
  36. 36.How many factors does 71 have? (a) 1 (b) 2 (c) 3 (d) 4
  37. 37.What is the smallest prime factor of 65? (a) 13 (b) 2 (c) 5 (d) 1
  38. 38.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
  39. 39.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  40. 40.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 6 (d) 8

Answer key

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

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