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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 110 · 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 319? (a) 1 (b) 11 (c) 2 (d) 29
  2. 2.How many factors does 48 have? (a) 10 (b) 9 (c) 11 (d) 8
  3. 3.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁵ × 3 × 5
  4. 4.How many factors does 73 have? (a) 2 (b) 3 (c) 1 (d) 4
  5. 5.How many factors does 29 have? (a) 3 (b) 1 (c) 4 (d) 2
  6. 6.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
  7. 7.How many factors does 27 have? (a) 4 (b) 5 (c) 3 (d) 2
  8. 8.How many factors does 14 have? (a) 2 (b) 3 (c) 4 (d) 5
  9. 9.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2⁴ × 3² × 5
  10. 10.How many prime numbers are there between 90 and 120? (a) 6 (b) 8 (c) 7 (d) 5
  11. 11.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  12. 12.How many factors does 51 have? (a) 3 (b) 2 (c) 4 (d) 5
  13. 13.How many prime numbers are there between 50 and 70? (a) 3 (b) 4 (c) 5 (d) 6
  14. 14.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5 (c) 2 × 3² × 5² (d) 2³ × 3² × 5
  15. 15.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3² (c) 2 × 3² (d) 2² × 3
  16. 16.How many factors does 102 have? (a) 7 (b) 9 (c) 8 (d) 6
  17. 17.What is the smallest prime factor of 57? (a) 1 (b) 19 (c) 3 (d) 2
  18. 18.What is the smallest prime factor of 49? (a) 7 (b) 3 (c) 2 (d) 1
  19. 19.What is the smallest prime factor of 85? (a) 1 (b) 2 (c) 17 (d) 5
  20. 20.How many factors does 68 have? (a) 4 (b) 7 (c) 5 (d) 6
  21. 21.What is the smallest prime factor of 121? (a) 2 (b) 1 (c) 3 (d) 11
  22. 22.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
  23. 23.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5 × 7
  24. 24.How many factors does 19 have? (a) 1 (b) 4 (c) 2 (d) 3
  25. 25.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 31 (d) 5
  26. 26.How many factors does 40 have? (a) 6 (b) 8 (c) 7 (d) 9
  27. 27.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 3 (d) 1
  28. 28.What is the prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2⁴ × 3²
  29. 29.How many factors does 26 have? (a) 5 (b) 2 (c) 4 (d) 3
  30. 30.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7²
  31. 31.How many factors does 12 have? (a) 4 (b) 7 (c) 6 (d) 5
  32. 32.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2 × 5 × 7³
  33. 33.How many factors does 38 have? (a) 4 (b) 3 (c) 5 (d) 2
  34. 34.How many factors does 88 have? (a) 6 (b) 8 (c) 7 (d) 9
  35. 35.How many factors does 97 have? (a) 3 (b) 1 (c) 2 (d) 4
  36. 36.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 1 (d) 3
  37. 37.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 4 (d) 5
  38. 38.What is the prime factorisation of 28? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
  39. 39.How many prime numbers are there between 90 and 100? (a) 1 (b) 0 (c) 3 (d) 2
  40. 40.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2³ × 7

Answer key

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

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