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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 134 · 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 85? (a) 1 (b) 5 (c) 17 (d) 2
  2. 2.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2⁵ × 3
  3. 3.What is the smallest prime factor of 133? (a) 7 (b) 19 (c) 2 (d) 1
  4. 4.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 6 (d) 4
  5. 5.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
  6. 6.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  7. 7.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 3 (d) 2
  8. 8.What is the smallest prime factor of 57? (a) 19 (b) 3 (c) 1 (d) 2
  9. 9.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
  10. 10.How many factors does 76 have? (a) 5 (b) 4 (c) 6 (d) 7
  11. 11.How many factors does 79 have? (a) 2 (b) 3 (c) 1 (d) 4
  12. 12.How many factors does 87 have? (a) 3 (b) 4 (c) 2 (d) 5
  13. 13.How many factors does 13 have? (a) 2 (b) 4 (c) 1 (d) 3
  14. 14.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 4 (d) 2
  15. 15.How many factors does 31 have? (a) 3 (b) 4 (c) 2 (d) 1
  16. 16.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 1 (d) 2
  17. 17.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 1 (d) 3
  18. 18.How many prime numbers are there between 60 and 90? (a) 8 (b) 9 (c) 6 (d) 7
  19. 19.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
  20. 20.What is the smallest prime factor of 121? (a) 2 (b) 3 (c) 11 (d) 1
  21. 21.How many prime numbers are there between 40 and 70? (a) 8 (b) 7 (c) 9 (d) 6
  22. 22.How many factors does 15 have? (a) 4 (b) 3 (c) 5 (d) 2
  23. 23.How many factors does 99 have? (a) 5 (b) 7 (c) 6 (d) 4
  24. 24.How many factors does 67 have? (a) 3 (b) 4 (c) 2 (d) 1
  25. 25.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  26. 26.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3² × 7 (d) 3 × 7
  27. 27.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
  28. 28.What is the smallest prime factor of 247? (a) 2 (b) 13 (c) 19 (d) 1
  29. 29.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2 × 7⁴
  30. 30.What is the smallest prime factor of 33? (a) 2 (b) 1 (c) 3 (d) 11
  31. 31.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 6 (d) 8
  32. 32.What is the smallest prime factor of 221? (a) 1 (b) 2 (c) 17 (d) 13
  33. 33.How many factors does 89 have? (a) 4 (b) 1 (c) 3 (d) 2
  34. 34.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2⁴ × 3 × 5
  35. 35.How many factors does 70 have? (a) 7 (b) 6 (c) 8 (d) 9
  36. 36.How many factors does 29 have? (a) 2 (b) 1 (c) 3 (d) 4
  37. 37.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7²
  38. 38.What is the prime factorisation of 12? (a) 2 × 3 (b) 2² × 3 (c) 2 × 3² (d) 2³ × 3
  39. 39.How many factors does 114 have? (a) 9 (b) 7 (c) 8 (d) 6
  40. 40.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 2 (d) 1

Answer key

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

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