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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 59 · 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 53 have? (a) 3 (b) 4 (c) 1 (d) 2
  2. 2.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 5 (d) 6
  3. 3.How many factors does 40 have? (a) 9 (b) 6 (c) 8 (d) 7
  4. 4.How many prime numbers are there between 80 and 110? (a) 7 (b) 6 (c) 8 (d) 9
  5. 5.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2⁵ × 3 (d) 2³ × 3
  6. 6.How many factors does 44 have? (a) 6 (b) 5 (c) 7 (d) 4
  7. 7.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 3 (d) 2
  8. 8.What is the prime factorisation of 72? (a) 2² × 3² (b) 2⁴ × 3² (c) 2³ × 3² (d) 2² × 3³
  9. 9.How many factors does 23 have? (a) 3 (b) 2 (c) 4 (d) 1
  10. 10.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 1 (d) 2
  11. 11.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2² × 7
  12. 12.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 2 (d) 1
  13. 13.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 5 (d) 4
  14. 14.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 9 (d) 8
  15. 15.How many factors does 115 have? (a) 3 (b) 4 (c) 2 (d) 5
  16. 16.How many factors does 112 have? (a) 8 (b) 11 (c) 9 (d) 10
  17. 17.What is the smallest prime factor of 35? (a) 7 (b) 2 (c) 5 (d) 1
  18. 18.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2 × 3 × 5
  19. 19.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  20. 20.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2³ × 5 (d) 2² × 5
  21. 21.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 3 (d) 1
  22. 22.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 6 (d) 8
  23. 23.How many factors does 13 have? (a) 2 (b) 1 (c) 4 (d) 3
  24. 24.How many factors does 106 have? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
  26. 26.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  27. 27.What is the smallest prime factor of 21? (a) 7 (b) 3 (c) 1 (d) 2
  28. 28.How many prime numbers are there between 40 and 60? (a) 7 (b) 5 (c) 4 (d) 6
  29. 29.What is the smallest prime factor of 49? (a) 3 (b) 1 (c) 7 (d) 2
  30. 30.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
  31. 31.How many factors does 61 have? (a) 1 (b) 2 (c) 3 (d) 4
  32. 32.How many factors does 16 have? (a) 5 (b) 6 (c) 3 (d) 4
  33. 33.How many factors does 90 have? (a) 10 (b) 11 (c) 13 (d) 12
  34. 34.How many factors does 63 have? (a) 5 (b) 7 (c) 4 (d) 6
  35. 35.How many factors does 98 have? (a) 6 (b) 4 (c) 5 (d) 7
  36. 36.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 3 (d) 1
  37. 37.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 7 (d) 9
  38. 38.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7 (c) 5³ × 7 (d) 5 × 7²
  39. 39.How many factors does 35 have? (a) 5 (b) 3 (c) 4 (d) 2
  40. 40.How many factors does 82 have? (a) 2 (b) 4 (c) 5 (d) 3

Answer key

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

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