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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 42 · 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 prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
  2. 2.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
  3. 3.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2 × 3² × 7³
  4. 4.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 8 (d) 7
  5. 5.How many factors does 40 have? (a) 6 (b) 7 (c) 8 (d) 9
  6. 6.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 1 (d) 3
  7. 7.How many factors does 110 have? (a) 8 (b) 7 (c) 9 (d) 6
  8. 8.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 7 (d) 6
  9. 9.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2² × 3 × 7
  10. 10.What is the smallest prime factor of 319? (a) 1 (b) 29 (c) 2 (d) 11
  11. 11.How many factors does 113 have? (a) 2 (b) 1 (c) 3 (d) 4
  12. 12.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 2 (d) 4
  13. 13.How many factors does 68 have? (a) 7 (b) 6 (c) 4 (d) 5
  14. 14.How many factors does 28 have? (a) 6 (b) 7 (c) 5 (d) 4
  15. 15.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  16. 16.How many factors does 95 have? (a) 2 (b) 5 (c) 4 (d) 3
  17. 17.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 7 (d) 2
  18. 18.How many prime numbers are there between 40 and 60? (a) 4 (b) 7 (c) 6 (d) 5
  19. 19.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 7 (d) 11
  20. 20.What is the smallest prime factor of 49? (a) 7 (b) 1 (c) 2 (d) 3
  21. 21.How many factors does 17 have? (a) 3 (b) 2 (c) 1 (d) 4
  22. 22.What is the smallest prime factor of 93? (a) 3 (b) 2 (c) 1 (d) 31
  23. 23.How many prime numbers are there between 20 and 40? (a) 4 (b) 5 (c) 3 (d) 6
  24. 24.What is the prime factorisation of 24? (a) 2² × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3³
  25. 25.How many factors does 97 have? (a) 4 (b) 2 (c) 1 (d) 3
  26. 26.How many factors does 49 have? (a) 1 (b) 2 (c) 4 (d) 3
  27. 27.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
  28. 28.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 1 (d) 2
  29. 29.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 5 (d) 3
  30. 30.How many factors does 58 have? (a) 2 (b) 5 (c) 3 (d) 4
  31. 31.How many factors does 52 have? (a) 6 (b) 7 (c) 4 (d) 5
  32. 32.How many factors does 88 have? (a) 6 (b) 9 (c) 7 (d) 8
  33. 33.How many factors does 70 have? (a) 9 (b) 7 (c) 8 (d) 6
  34. 34.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 6 (d) 5
  35. 35.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2⁵ × 3
  36. 36.How many factors does 16 have? (a) 5 (b) 6 (c) 3 (d) 4
  37. 37.How many factors does 83 have? (a) 4 (b) 2 (c) 3 (d) 1
  38. 38.How many factors does 80 have? (a) 8 (b) 11 (c) 9 (d) 10
  39. 39.How many factors does 57 have? (a) 2 (b) 4 (c) 5 (d) 3
  40. 40.How many factors does 29 have? (a) 1 (b) 4 (c) 2 (d) 3

Answer key

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

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