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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 162 · 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 factors does 83 have? (a) 1 (b) 3 (c) 4 (d) 2
  2. 2.How many factors does 22 have? (a) 3 (b) 2 (c) 4 (d) 5
  3. 3.How many prime numbers are there between 80 and 100? (a) 2 (b) 4 (c) 5 (d) 3
  4. 4.How many factors does 65 have? (a) 5 (b) 3 (c) 4 (d) 2
  5. 5.What is the prime factorisation of 14? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
  6. 6.How many factors does 107 have? (a) 3 (b) 2 (c) 4 (d) 1
  7. 7.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 4 (d) 5
  8. 8.What is the smallest prime factor of 119? (a) 17 (b) 1 (c) 2 (d) 7
  9. 9.How many prime numbers are there between 80 and 110? (a) 6 (b) 9 (c) 8 (d) 7
  10. 10.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
  11. 11.How many prime numbers are there between 90 and 100? (a) 3 (b) 1 (c) 2 (d) 0
  12. 12.How many factors does 45 have? (a) 7 (b) 5 (c) 6 (d) 4
  13. 13.How many factors does 14 have? (a) 2 (b) 3 (c) 5 (d) 4
  14. 14.What is the prime factorisation of 45? (a) 3 × 5² (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5
  15. 15.What is the smallest prime factor of 203? (a) 7 (b) 1 (c) 29 (d) 2
  16. 16.What is the prime factorisation of 35? (a) 5 × 7² (b) 5² × 7 (c) 5³ × 7 (d) 5 × 7
  17. 17.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 11 (d) 17
  18. 18.How many factors does 26 have? (a) 2 (b) 4 (c) 5 (d) 3
  19. 19.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2⁵ × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  20. 20.What is the smallest prime factor of 341? (a) 11 (b) 1 (c) 2 (d) 31
  21. 21.How many factors does 32 have? (a) 7 (b) 6 (c) 5 (d) 4
  22. 22.How many prime numbers are there between 50 and 70? (a) 5 (b) 4 (c) 3 (d) 6
  23. 23.How many prime numbers are there between 40 and 60? (a) 7 (b) 5 (c) 4 (d) 6
  24. 24.What is the smallest prime factor of 299? (a) 2 (b) 23 (c) 1 (d) 13
  25. 25.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 7 (d) 1
  26. 26.How many factors does 37 have? (a) 2 (b) 4 (c) 3 (d) 1
  27. 27.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 6 (d) 8
  28. 28.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 29 (d) 3
  29. 29.What is the smallest prime factor of 115? (a) 2 (b) 5 (c) 23 (d) 1
  30. 30.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2² × 5 (c) 2⁴ × 5 (d) 2³ × 5
  31. 31.What is the smallest prime factor of 169? (a) 1 (b) 2 (c) 3 (d) 13
  32. 32.How many factors does 96 have? (a) 12 (b) 13 (c) 10 (d) 11
  33. 33.How many factors does 43 have? (a) 3 (b) 2 (c) 1 (d) 4
  34. 34.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 5 (d) 4
  35. 35.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  36. 36.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 7 (d) 6
  37. 37.How many factors does 68 have? (a) 7 (b) 4 (c) 6 (d) 5
  38. 38.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  39. 39.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  40. 40.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2 × 3³ (c) 2⁴ × 3 (d) 2² × 3

Answer key

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

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