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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 100 · 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 126? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  2. 2.How many factors does 38 have? (a) 5 (b) 2 (c) 3 (d) 4
  3. 3.What is the smallest prime factor of 35? (a) 5 (b) 1 (c) 2 (d) 7
  4. 4.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5³ (d) 2⁴ × 5
  5. 5.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7² (c) 2 × 7 (d) 2² × 7
  6. 6.How many factors does 84 have? (a) 13 (b) 11 (c) 10 (d) 12
  7. 7.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 1 (d) 2
  8. 8.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  9. 9.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 7 (d) 1
  10. 10.How many factors does 45 have? (a) 4 (b) 5 (c) 6 (d) 7
  11. 11.How many prime numbers are there between 70 and 90? (a) 6 (b) 7 (c) 5 (d) 4
  12. 12.How many factors does 114 have? (a) 7 (b) 8 (c) 9 (d) 6
  13. 13.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 5 (d) 6
  14. 14.How many prime numbers are there between 40 and 70? (a) 7 (b) 8 (c) 9 (d) 6
  15. 15.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
  16. 16.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2⁵ × 7
  17. 17.How many factors does 17 have? (a) 4 (b) 1 (c) 3 (d) 2
  18. 18.How many factors does 80 have? (a) 9 (b) 10 (c) 11 (d) 8
  19. 19.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2
  20. 20.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2³ × 3 (c) 2⁴ × 3 (d) 2² × 3
  21. 21.What is the smallest prime factor of 57? (a) 19 (b) 3 (c) 2 (d) 1
  22. 22.How many factors does 116 have? (a) 4 (b) 6 (c) 7 (d) 5
  23. 23.How many factors does 35 have? (a) 4 (b) 3 (c) 2 (d) 5
  24. 24.How many factors does 64 have? (a) 6 (b) 5 (c) 8 (d) 7
  25. 25.What is the smallest prime factor of 253? (a) 1 (b) 23 (c) 11 (d) 2
  26. 26.How many factors does 90 have? (a) 10 (b) 12 (c) 13 (d) 11
  27. 27.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 7 (d) 1
  28. 28.What is the smallest prime factor of 55? (a) 2 (b) 5 (c) 1 (d) 11
  29. 29.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 4 (d) 6
  30. 30.What is the smallest prime factor of 203? (a) 7 (b) 2 (c) 1 (d) 29
  31. 31.How many factors does 88 have? (a) 7 (b) 8 (c) 6 (d) 9
  32. 32.What is the prime factorisation of 12? (a) 2 × 3² (b) 2³ × 3 (c) 2² × 3 (d) 2 × 3
  33. 33.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3 (c) 2 × 3² (d) 2² × 3²
  34. 34.How many factors does 102 have? (a) 6 (b) 9 (c) 7 (d) 8
  35. 35.What is the smallest prime factor of 299? (a) 13 (b) 2 (c) 23 (d) 1
  36. 36.How many prime numbers are there between 30 and 40? (a) 1 (b) 3 (c) 4 (d) 2
  37. 37.What is the smallest prime factor of 155? (a) 5 (b) 31 (c) 2 (d) 1
  38. 38.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 11 (d) 29
  39. 39.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
  40. 40.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 5 (d) 7

Answer key

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

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