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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 84 · 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 factors does 75 have? (a) 5 (b) 7 (c) 6 (d) 4
  2. 2.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2
  3. 3.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 4 (d) 1
  4. 4.What is the prime factorisation of 12? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3² (d) 2 × 3
  5. 5.What is the smallest prime factor of 55? (a) 5 (b) 2 (c) 1 (d) 11
  6. 6.What is the smallest prime factor of 187? (a) 2 (b) 17 (c) 11 (d) 1
  7. 7.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2³ × 3²
  8. 8.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7² (d) 5 × 7
  9. 9.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7³
  10. 10.How many factors does 96 have? (a) 10 (b) 11 (c) 13 (d) 12
  11. 11.How many factors does 25 have? (a) 1 (b) 4 (c) 3 (d) 2
  12. 12.What is the smallest prime factor of 85? (a) 5 (b) 2 (c) 1 (d) 17
  13. 13.How many factors does 52 have? (a) 4 (b) 6 (c) 5 (d) 7
  14. 14.How many factors does 19 have? (a) 4 (b) 2 (c) 1 (d) 3
  15. 15.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 0 (d) 3
  16. 16.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 2 (d) 3
  17. 17.What is the smallest prime factor of 119? (a) 2 (b) 1 (c) 7 (d) 17
  18. 18.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  19. 19.How many factors does 78 have? (a) 7 (b) 6 (c) 9 (d) 8
  20. 20.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
  21. 21.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 2 (d) 11
  22. 22.How many prime numbers are there between 50 and 70? (a) 4 (b) 3 (c) 5 (d) 6
  23. 23.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2³ × 3²
  24. 24.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7
  26. 26.How many factors does 24 have? (a) 6 (b) 8 (c) 7 (d) 9
  27. 27.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 10 (d) 7
  28. 28.How many factors does 30 have? (a) 8 (b) 6 (c) 9 (d) 7
  29. 29.How many factors does 95 have? (a) 5 (b) 3 (c) 4 (d) 2
  30. 30.What is the smallest prime factor of 203? (a) 2 (b) 7 (c) 29 (d) 1
  31. 31.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
  32. 32.How many factors does 73 have? (a) 4 (b) 3 (c) 1 (d) 2
  33. 33.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2² × 5 (c) 2³ × 5 (d) 2⁴ × 5
  34. 34.How many factors does 67 have? (a) 3 (b) 1 (c) 4 (d) 2
  35. 35.How many factors does 117 have? (a) 4 (b) 5 (c) 7 (d) 6
  36. 36.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
  37. 37.How many factors does 39 have? (a) 4 (b) 5 (c) 3 (d) 2
  38. 38.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2⁴ × 3 (d) 2³ × 3
  39. 39.How many prime numbers are there between 70 and 90? (a) 4 (b) 6 (c) 7 (d) 5
  40. 40.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 3 (d) 4

Answer key

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

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