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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 184 · 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 prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  2. 2.How many factors does 101 have? (a) 1 (b) 3 (c) 2 (d) 4
  3. 3.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
  4. 4.How many factors does 28 have? (a) 5 (b) 6 (c) 4 (d) 7
  5. 5.How many prime numbers are there between 60 and 80? (a) 6 (b) 5 (c) 7 (d) 4
  6. 6.What is the smallest prime factor of 253? (a) 11 (b) 1 (c) 23 (d) 2
  7. 7.How many prime numbers are there between 10 and 40? (a) 8 (b) 7 (c) 10 (d) 9
  8. 8.How many factors does 84 have? (a) 11 (b) 10 (c) 12 (d) 13
  9. 9.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5³ (d) 2² × 3 × 5
  10. 10.How many factors does 49 have? (a) 3 (b) 4 (c) 2 (d) 1
  11. 11.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
  12. 12.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
  13. 13.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 2 (d) 5
  14. 14.How many prime numbers are there between 50 and 60? (a) 1 (b) 2 (c) 3 (d) 4
  15. 15.How many factors does 100 have? (a) 8 (b) 9 (c) 10 (d) 7
  16. 16.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
  17. 17.What is the smallest prime factor of 319? (a) 11 (b) 2 (c) 1 (d) 29
  18. 18.How many factors does 30 have? (a) 7 (b) 8 (c) 9 (d) 6
  19. 19.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
  20. 20.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 8 (d) 9
  21. 21.How many factors does 74 have? (a) 5 (b) 3 (c) 2 (d) 4
  22. 22.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  23. 23.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3 × 7
  24. 24.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 2 (d) 7
  25. 25.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 11 (d) 1
  26. 26.How many factors does 97 have? (a) 2 (b) 3 (c) 1 (d) 4
  27. 27.How many factors does 27 have? (a) 3 (b) 2 (c) 5 (d) 4
  28. 28.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 9 (d) 7
  29. 29.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁵ × 5 × 7
  30. 30.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
  31. 31.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 2 (d) 7
  32. 32.How many factors does 32 have? (a) 5 (b) 6 (c) 4 (d) 7
  33. 33.What is the smallest prime factor of 49? (a) 7 (b) 1 (c) 2 (d) 3
  34. 34.How many factors does 52 have? (a) 7 (b) 6 (c) 5 (d) 4
  35. 35.How many prime numbers are there between 30 and 40? (a) 4 (b) 2 (c) 3 (d) 1
  36. 36.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
  37. 37.How many prime numbers are there between 90 and 110? (a) 7 (b) 4 (c) 5 (d) 6
  38. 38.What is the smallest prime factor of 403? (a) 2 (b) 13 (c) 31 (d) 1
  39. 39.How many factors does 63 have? (a) 6 (b) 7 (c) 5 (d) 4
  40. 40.What is the smallest prime factor of 115? (a) 5 (b) 1 (c) 23 (d) 2

Answer key

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

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