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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 65 · 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 14 have? (a) 2 (b) 5 (c) 3 (d) 4
  2. 2.How many prime numbers are there between 70 and 100? (a) 6 (b) 5 (c) 7 (d) 8
  3. 3.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2⁵ × 7
  4. 4.How many prime numbers are there between 90 and 120? (a) 7 (b) 6 (c) 8 (d) 5
  5. 5.How many factors does 100 have? (a) 8 (b) 10 (c) 9 (d) 7
  6. 6.How many factors does 70 have? (a) 8 (b) 7 (c) 6 (d) 9
  7. 7.How many factors does 21 have? (a) 2 (b) 3 (c) 5 (d) 4
  8. 8.What is the smallest prime factor of 115? (a) 2 (b) 1 (c) 23 (d) 5
  9. 9.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
  10. 10.What is the smallest prime factor of 403? (a) 13 (b) 2 (c) 1 (d) 31
  11. 11.What is the smallest prime factor of 55? (a) 5 (b) 11 (c) 1 (d) 2
  12. 12.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 5 (d) 2
  13. 13.How many factors does 110 have? (a) 6 (b) 8 (c) 7 (d) 9
  14. 14.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 3 (d) 6
  15. 15.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 8 (d) 5
  16. 16.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 11 (d) 1
  17. 17.How many factors does 40 have? (a) 6 (b) 9 (c) 8 (d) 7
  18. 18.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7² (c) 2 × 7 (d) 2² × 7
  19. 19.How many factors does 107 have? (a) 1 (b) 4 (c) 2 (d) 3
  20. 20.How many factors does 89 have? (a) 2 (b) 4 (c) 1 (d) 3
  21. 21.What is the smallest prime factor of 39? (a) 13 (b) 1 (c) 2 (d) 3
  22. 22.How many factors does 42 have? (a) 9 (b) 6 (c) 8 (d) 7
  23. 23.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 3 (d) 29
  24. 24.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
  25. 25.What is the prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2 × 5² (d) 2³ × 5
  26. 26.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7²
  27. 27.How many prime numbers are there between 90 and 100? (a) 0 (b) 2 (c) 1 (d) 3
  28. 28.How many factors does 52 have? (a) 7 (b) 4 (c) 6 (d) 5
  29. 29.What is the smallest prime factor of 217? (a) 7 (b) 2 (c) 31 (d) 1
  30. 30.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2⁵ × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  31. 31.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 4 (d) 5
  32. 32.How many factors does 96 have? (a) 11 (b) 13 (c) 12 (d) 10
  33. 33.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 11 (d) 2
  34. 34.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 2 (d) 13
  35. 35.What is the smallest prime factor of 85? (a) 17 (b) 5 (c) 2 (d) 1
  36. 36.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 1 (d) 2
  37. 37.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 8 (d) 9
  38. 38.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
  39. 39.How many factors does 97 have? (a) 1 (b) 4 (c) 2 (d) 3
  40. 40.What is the smallest prime factor of 51? (a) 2 (b) 17 (c) 3 (d) 1

Answer key

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

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