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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 131 · 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 95? (a) 2 (b) 19 (c) 1 (d) 5
  2. 2.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 2 (d) 4
  3. 3.How many factors does 112 have? (a) 9 (b) 11 (c) 8 (d) 10
  4. 4.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 5 (d) 8
  5. 5.How many factors does 94 have? (a) 4 (b) 2 (c) 3 (d) 5
  6. 6.What is the smallest prime factor of 403? (a) 1 (b) 31 (c) 13 (d) 2
  7. 7.How many prime numbers are there between 50 and 80? (a) 7 (b) 9 (c) 6 (d) 8
  8. 8.How many prime numbers are there between 40 and 70? (a) 9 (b) 8 (c) 7 (d) 6
  9. 9.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
  10. 10.How many factors does 21 have? (a) 5 (b) 2 (c) 3 (d) 4
  11. 11.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  12. 12.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  13. 13.How many factors does 101 have? (a) 2 (b) 3 (c) 1 (d) 4
  14. 14.How many factors does 56 have? (a) 8 (b) 7 (c) 9 (d) 6
  15. 15.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  16. 16.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3² (c) 2 × 3³ (d) 2² × 3
  17. 17.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 4 (d) 5
  18. 18.What is the smallest prime factor of 203? (a) 2 (b) 1 (c) 7 (d) 29
  19. 19.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 3 (d) 2
  20. 20.What is the smallest prime factor of 187? (a) 17 (b) 2 (c) 1 (d) 11
  21. 21.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3 × 5 × 7²
  22. 22.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  23. 23.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7³ (d) 2⁴ × 3² × 7
  24. 24.How many factors does 45 have? (a) 5 (b) 4 (c) 7 (d) 6
  25. 25.How many factors does 116 have? (a) 5 (b) 6 (c) 4 (d) 7
  26. 26.How many factors does 41 have? (a) 4 (b) 1 (c) 3 (d) 2
  27. 27.How many factors does 36 have? (a) 8 (b) 9 (c) 10 (d) 7
  28. 28.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  29. 29.How many factors does 89 have? (a) 1 (b) 3 (c) 2 (d) 4
  30. 30.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2⁵ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2³ × 5 × 7
  31. 31.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 5 (d) 1
  32. 32.How many prime numbers are there between 40 and 60? (a) 4 (b) 6 (c) 7 (d) 5
  33. 33.What is the smallest prime factor of 93? (a) 2 (b) 3 (c) 31 (d) 1
  34. 34.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3³
  35. 35.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
  36. 36.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
  37. 37.How many prime numbers are there between 90 and 110? (a) 7 (b) 6 (c) 4 (d) 5
  38. 38.How many prime numbers are there between 70 and 90? (a) 7 (b) 6 (c) 4 (d) 5
  39. 39.What is the smallest prime factor of 33? (a) 1 (b) 3 (c) 11 (d) 2
  40. 40.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4

Answer key

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

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