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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 185 · 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 74 have? (a) 2 (b) 3 (c) 4 (d) 5
  2. 2.How many factors does 48 have? (a) 8 (b) 11 (c) 10 (d) 9
  3. 3.How many factors does 111 have? (a) 3 (b) 2 (c) 4 (d) 5
  4. 4.How many factors does 58 have? (a) 2 (b) 4 (c) 3 (d) 5
  5. 5.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 17 (d) 2
  6. 6.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2⁴ × 5 × 7 (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  7. 7.How many factors does 33 have? (a) 5 (b) 2 (c) 3 (d) 4
  8. 8.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 2 (d) 1
  9. 9.What is the smallest prime factor of 145? (a) 1 (b) 2 (c) 5 (d) 29
  10. 10.How many factors does 18 have? (a) 7 (b) 6 (c) 5 (d) 4
  11. 11.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  12. 12.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
  13. 13.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 1 (d) 4
  14. 14.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2² × 3 × 7
  15. 15.How many factors does 12 have? (a) 4 (b) 5 (c) 7 (d) 6
  16. 16.How many prime numbers are there between 40 and 70? (a) 9 (b) 8 (c) 7 (d) 6
  17. 17.What is the prime factorisation of 21? (a) 3 × 7 (b) 3 × 7² (c) 3² × 7 (d) 3³ × 7
  18. 18.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 1 (d) 11
  19. 19.How many factors does 73 have? (a) 4 (b) 2 (c) 3 (d) 1
  20. 20.What is the smallest prime factor of 377? (a) 2 (b) 1 (c) 13 (d) 29
  21. 21.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2² × 3² × 7
  22. 22.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 5 (d) 4
  23. 23.How many factors does 38 have? (a) 2 (b) 3 (c) 5 (d) 4
  24. 24.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁵ × 5 × 7
  25. 25.How many prime numbers are there between 30 and 60? (a) 9 (b) 6 (c) 8 (d) 7
  26. 26.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2 × 5⁴ (d) 2⁵ × 5
  27. 27.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
  28. 28.How many factors does 56 have? (a) 8 (b) 6 (c) 9 (d) 7
  29. 29.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2² × 3² × 5
  30. 30.How many factors does 20 have? (a) 4 (b) 5 (c) 6 (d) 7
  31. 31.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5
  32. 32.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 29 (d) 3
  33. 33.What is the smallest prime factor of 115? (a) 2 (b) 1 (c) 5 (d) 23
  34. 34.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2² × 3 × 7
  35. 35.How many factors does 84 have? (a) 10 (b) 11 (c) 13 (d) 12
  36. 36.What is the smallest prime factor of 49? (a) 3 (b) 1 (c) 2 (d) 7
  37. 37.How many factors does 119 have? (a) 5 (b) 3 (c) 2 (d) 4
  38. 38.How many factors does 23 have? (a) 2 (b) 1 (c) 4 (d) 3
  39. 39.How many prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 7 (d) 9
  40. 40.How many factors does 39 have? (a) 3 (b) 2 (c) 4 (d) 5

Answer key

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

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