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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 140 · 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 403? (a) 13 (b) 2 (c) 1 (d) 31
  2. 2.How many factors does 100 have? (a) 7 (b) 10 (c) 8 (d) 9
  3. 3.What is the smallest prime factor of 169? (a) 13 (b) 2 (c) 3 (d) 1
  4. 4.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
  5. 5.What is the smallest prime factor of 33? (a) 2 (b) 1 (c) 11 (d) 3
  6. 6.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3² (c) 2³ × 3² (d) 2² × 3³
  7. 7.How many factors does 25 have? (a) 3 (b) 1 (c) 2 (d) 4
  8. 8.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 1 (d) 2
  9. 9.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2 × 3³ (d) 2² × 3
  10. 10.What is the smallest prime factor of 85? (a) 2 (b) 5 (c) 17 (d) 1
  11. 11.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  12. 12.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 6 (d) 5
  13. 13.What is the smallest prime factor of 35? (a) 2 (b) 7 (c) 5 (d) 1
  14. 14.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3 × 7
  15. 15.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2⁴ × 5 (d) 2 × 5⁴
  16. 16.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 9 (d) 7
  17. 17.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 9 (d) 10
  18. 18.What is the smallest prime factor of 115? (a) 2 (b) 5 (c) 1 (d) 23
  19. 19.How many factors does 21 have? (a) 3 (b) 2 (c) 4 (d) 5
  20. 20.How many factors does 46 have? (a) 2 (b) 3 (c) 5 (d) 4
  21. 21.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3 × 5
  22. 22.How many factors does 43 have? (a) 1 (b) 3 (c) 4 (d) 2
  23. 23.How many factors does 87 have? (a) 2 (b) 5 (c) 3 (d) 4
  24. 24.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 5 (d) 6
  25. 25.How many factors does 85 have? (a) 2 (b) 3 (c) 5 (d) 4
  26. 26.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 2 (d) 4
  27. 27.How many factors does 19 have? (a) 4 (b) 1 (c) 3 (d) 2
  28. 28.How many factors does 84 have? (a) 12 (b) 13 (c) 11 (d) 10
  29. 29.How many factors does 47 have? (a) 4 (b) 3 (c) 2 (d) 1
  30. 30.How many factors does 57 have? (a) 2 (b) 5 (c) 3 (d) 4
  31. 31.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 17 (d) 1
  32. 32.How many factors does 36 have? (a) 8 (b) 10 (c) 7 (d) 9
  33. 33.How many factors does 40 have? (a) 6 (b) 9 (c) 7 (d) 8
  34. 34.What is the smallest prime factor of 209? (a) 11 (b) 19 (c) 2 (d) 1
  35. 35.How many factors does 68 have? (a) 5 (b) 4 (c) 6 (d) 7
  36. 36.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 1 (d) 7
  37. 37.What is the prime factorisation of 56? (a) 2² × 7 (b) 2⁴ × 7 (c) 2 × 7³ (d) 2³ × 7
  38. 38.How many factors does 24 have? (a) 7 (b) 8 (c) 9 (d) 6
  39. 39.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2⁴ × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  40. 40.How many factors does 30 have? (a) 9 (b) 8 (c) 7 (d) 6

Answer key

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

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