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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 135 · 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 55? (a) 1 (b) 11 (c) 2 (d) 5
  2. 2.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 5 (d) 31
  3. 3.How many prime numbers are there between 90 and 120? (a) 5 (b) 6 (c) 8 (d) 7
  4. 4.How many prime numbers are there between 60 and 80? (a) 4 (b) 7 (c) 5 (d) 6
  5. 5.What is the smallest prime factor of 145? (a) 29 (b) 1 (c) 2 (d) 5
  6. 6.How many prime numbers are there between 50 and 60? (a) 4 (b) 3 (c) 2 (d) 1
  7. 7.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2⁵ × 5 × 7
  8. 8.How many factors does 102 have? (a) 6 (b) 8 (c) 7 (d) 9
  9. 9.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 4 (d) 7
  10. 10.How many factors does 16 have? (a) 6 (b) 3 (c) 5 (d) 4
  11. 11.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  12. 12.What is the smallest prime factor of 161? (a) 1 (b) 23 (c) 7 (d) 2
  13. 13.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 1 (d) 7
  14. 14.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5 × 7
  15. 15.How many prime numbers are there between 30 and 60? (a) 7 (b) 6 (c) 9 (d) 8
  16. 16.How many factors does 72 have? (a) 12 (b) 10 (c) 13 (d) 11
  17. 17.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 1 (d) 3
  18. 18.What is the smallest prime factor of 87? (a) 29 (b) 2 (c) 1 (d) 3
  19. 19.How many prime numbers are there between 30 and 50? (a) 5 (b) 4 (c) 7 (d) 6
  20. 20.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 13 (d) 11
  21. 21.How many factors does 37 have? (a) 4 (b) 3 (c) 2 (d) 1
  22. 22.How many factors does 47 have? (a) 3 (b) 1 (c) 4 (d) 2
  23. 23.What is the prime factorisation of 20? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5² (d) 2 × 5
  24. 24.What is the smallest prime factor of 21? (a) 2 (b) 7 (c) 3 (d) 1
  25. 25.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 4 (d) 2
  26. 26.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 13 (d) 1
  27. 27.What is the smallest prime factor of 121? (a) 1 (b) 11 (c) 2 (d) 3
  28. 28.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 9 (d) 6
  29. 29.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
  30. 30.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7 (c) 2 × 7² (d) 2³ × 7
  31. 31.How many factors does 110 have? (a) 9 (b) 6 (c) 8 (d) 7
  32. 32.How many factors does 113 have? (a) 3 (b) 1 (c) 4 (d) 2
  33. 33.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2 × 3²
  34. 34.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 6 (d) 3
  35. 35.How many factors does 96 have? (a) 10 (b) 12 (c) 13 (d) 11
  36. 36.How many factors does 99 have? (a) 6 (b) 4 (c) 7 (d) 5
  37. 37.How many factors does 32 have? (a) 4 (b) 7 (c) 6 (d) 5
  38. 38.How many factors does 51 have? (a) 5 (b) 4 (c) 2 (d) 3
  39. 39.How many factors does 48 have? (a) 8 (b) 9 (c) 11 (d) 10
  40. 40.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁵ × 3 × 7 (d) 2³ × 3 × 7

Answer key

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

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