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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 4 · 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 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  2. 2.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 7 (d) 1
  3. 3.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
  4. 4.What is the smallest prime factor of 51? (a) 3 (b) 17 (c) 1 (d) 2
  5. 5.What is the smallest prime factor of 377? (a) 13 (b) 1 (c) 2 (d) 29
  6. 6.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 6 (d) 7
  7. 7.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  8. 8.How many factors does 85 have? (a) 4 (b) 3 (c) 2 (d) 5
  9. 9.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  10. 10.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁵ × 3 × 7 (d) 2 × 3 × 7⁴
  11. 11.What is the smallest prime factor of 57? (a) 1 (b) 2 (c) 3 (d) 19
  12. 12.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2³ × 7 (c) 2⁴ × 7 (d) 2 × 7⁴
  13. 13.What is the prime factorisation of 35? (a) 5 × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5² × 7
  14. 14.How many factors does 36 have? (a) 8 (b) 7 (c) 10 (d) 9
  15. 15.What is the smallest prime factor of 115? (a) 5 (b) 2 (c) 23 (d) 1
  16. 16.How many prime numbers are there between 30 and 40? (a) 4 (b) 1 (c) 3 (d) 2
  17. 17.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7 (c) 2³ × 7 (d) 2 × 7²
  18. 18.How many factors does 90 have? (a) 13 (b) 12 (c) 10 (d) 11
  19. 19.How many factors does 64 have? (a) 8 (b) 5 (c) 7 (d) 6
  20. 20.How many factors does 41 have? (a) 4 (b) 1 (c) 2 (d) 3
  21. 21.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 31 (d) 5
  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 63 have? (a) 7 (b) 6 (c) 4 (d) 5
  24. 24.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  25. 25.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 8 (d) 9
  26. 26.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2² × 3² (d) 2 × 3³
  27. 27.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 4 (d) 3
  28. 28.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
  29. 29.How many factors does 87 have? (a) 2 (b) 3 (c) 5 (d) 4
  30. 30.How many factors does 55 have? (a) 3 (b) 4 (c) 5 (d) 2
  31. 31.How many factors does 81 have? (a) 5 (b) 6 (c) 3 (d) 4
  32. 32.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
  33. 33.What is the smallest prime factor of 35? (a) 7 (b) 1 (c) 5 (d) 2
  34. 34.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 2 (d) 1
  35. 35.How many factors does 89 have? (a) 4 (b) 1 (c) 3 (d) 2
  36. 36.How many factors does 98 have? (a) 7 (b) 5 (c) 4 (d) 6
  37. 37.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 2 (d) 7
  38. 38.How many prime numbers are there between 90 and 100? (a) 3 (b) 2 (c) 0 (d) 1
  39. 39.What is the prime factorisation of 63? (a) 3 × 7² (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7
  40. 40.How many factors does 58 have? (a) 5 (b) 3 (c) 2 (d) 4

Answer key

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

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