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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 56 · 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 18 have? (a) 6 (b) 4 (c) 7 (d) 5
  2. 2.How many factors does 59 have? (a) 4 (b) 2 (c) 3 (d) 1
  3. 3.How many factors does 64 have? (a) 6 (b) 5 (c) 8 (d) 7
  4. 4.What is the smallest prime factor of 95? (a) 5 (b) 1 (c) 2 (d) 19
  5. 5.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3² (c) 2 × 3² (d) 2² × 3
  6. 6.How many factors does 104 have? (a) 9 (b) 7 (c) 8 (d) 6
  7. 7.What is the smallest prime factor of 33? (a) 2 (b) 11 (c) 1 (d) 3
  8. 8.What is the smallest prime factor of 161? (a) 2 (b) 7 (c) 1 (d) 23
  9. 9.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 6 (d) 7
  10. 10.What is the smallest prime factor of 155? (a) 31 (b) 1 (c) 2 (d) 5
  11. 11.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2² × 3 × 7
  12. 12.How many factors does 58 have? (a) 2 (b) 4 (c) 5 (d) 3
  13. 13.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2³ × 7
  14. 14.What is the smallest prime factor of 299? (a) 13 (b) 1 (c) 23 (d) 2
  15. 15.What is the smallest prime factor of 169? (a) 3 (b) 2 (c) 1 (d) 13
  16. 16.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2² × 7
  17. 17.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 5 (d) 6
  18. 18.How many factors does 98 have? (a) 6 (b) 5 (c) 4 (d) 7
  19. 19.How many factors does 36 have? (a) 9 (b) 8 (c) 7 (d) 10
  20. 20.What is the smallest prime factor of 143? (a) 11 (b) 2 (c) 13 (d) 1
  21. 21.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2³ × 3 × 7 (d) 2² × 3 × 7
  22. 22.How many prime numbers are there between 40 and 60? (a) 7 (b) 5 (c) 4 (d) 6
  23. 23.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  24. 24.How many factors does 19 have? (a) 1 (b) 4 (c) 3 (d) 2
  25. 25.How many factors does 38 have? (a) 2 (b) 5 (c) 3 (d) 4
  26. 26.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 2 (d) 3
  27. 27.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5
  28. 28.What is the prime factorisation of 72? (a) 2² × 3² (b) 2² × 3³ (c) 2³ × 3² (d) 2⁴ × 3²
  29. 29.What is the smallest prime factor of 55? (a) 5 (b) 11 (c) 1 (d) 2
  30. 30.How many factors does 22 have? (a) 2 (b) 3 (c) 4 (d) 5
  31. 31.How many factors does 21 have? (a) 3 (b) 4 (c) 5 (d) 2
  32. 32.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
  33. 33.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5² (c) 2 × 5 (d) 2² × 5
  34. 34.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2³ × 5
  35. 35.How many factors does 39 have? (a) 3 (b) 5 (c) 4 (d) 2
  36. 36.How many factors does 100 have? (a) 7 (b) 8 (c) 10 (d) 9
  37. 37.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2 × 3² × 7³ (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
  38. 38.What is the prime factorisation of 360? (a) 2³ × 3² × 5 (b) 2 × 3² × 5³ (c) 2⁴ × 3² × 5 (d) 2² × 3² × 5
  39. 39.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3 × 7 (d) 3² × 7
  40. 40.How many factors does 13 have? (a) 3 (b) 1 (c) 2 (d) 4

Answer key

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

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