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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 68 · 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 50 and 70? (a) 5 (b) 3 (c) 4 (d) 6
  2. 2.What is the smallest prime factor of 155? (a) 31 (b) 5 (c) 1 (d) 2
  3. 3.What is the smallest prime factor of 253? (a) 11 (b) 1 (c) 23 (d) 2
  4. 4.What is the smallest prime factor of 115? (a) 1 (b) 5 (c) 23 (d) 2
  5. 5.How many factors does 23 have? (a) 4 (b) 3 (c) 1 (d) 2
  6. 6.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 5 (d) 6
  7. 7.What is the smallest prime factor of 35? (a) 1 (b) 2 (c) 5 (d) 7
  8. 8.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  9. 9.How many prime numbers are there between 90 and 110? (a) 7 (b) 5 (c) 4 (d) 6
  10. 10.How many factors does 76 have? (a) 7 (b) 5 (c) 6 (d) 4
  11. 11.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2
  12. 12.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
  13. 13.How many prime numbers are there between 40 and 60? (a) 4 (b) 7 (c) 6 (d) 5
  14. 14.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2 × 5 (d) 2³ × 5
  15. 15.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2⁴ × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
  16. 16.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2² × 3⁴ (c) 2⁴ × 3² (d) 2⁵ × 3²
  17. 17.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 5 (d) 7
  18. 18.How many factors does 54 have? (a) 6 (b) 9 (c) 8 (d) 7
  19. 19.How many factors does 38 have? (a) 2 (b) 3 (c) 5 (d) 4
  20. 20.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2⁵ × 5
  21. 21.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 7 (d) 10
  22. 22.How many factors does 35 have? (a) 2 (b) 5 (c) 3 (d) 4
  23. 23.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 2 (d) 4
  24. 24.How many factors does 91 have? (a) 3 (b) 2 (c) 5 (d) 4
  25. 25.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2 × 3² × 7³
  26. 26.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2 × 7⁴
  27. 27.How many factors does 119 have? (a) 2 (b) 5 (c) 4 (d) 3
  28. 28.What is the smallest prime factor of 39? (a) 3 (b) 1 (c) 2 (d) 13
  29. 29.How many factors does 63 have? (a) 7 (b) 4 (c) 5 (d) 6
  30. 30.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 4 (d) 3
  31. 31.What is the smallest prime factor of 209? (a) 1 (b) 19 (c) 2 (d) 11
  32. 32.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  33. 33.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  34. 34.What is the smallest prime factor of 33? (a) 2 (b) 1 (c) 3 (d) 11
  35. 35.How many prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 9 (d) 7
  36. 36.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
  37. 37.How many factors does 19 have? (a) 1 (b) 2 (c) 4 (d) 3
  38. 38.What is the smallest prime factor of 95? (a) 5 (b) 19 (c) 1 (d) 2
  39. 39.How many factors does 89 have? (a) 4 (b) 1 (c) 2 (d) 3
  40. 40.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 3 (d) 5

Answer key

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

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