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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 115 · 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 360? (a) 2³ × 3² × 5 (b) 2 × 3² × 5³ (c) 2² × 3² × 5 (d) 2⁴ × 3² × 5
  2. 2.How many factors does 96 have? (a) 10 (b) 13 (c) 12 (d) 11
  3. 3.What is the smallest prime factor of 217? (a) 7 (b) 31 (c) 1 (d) 2
  4. 4.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3 × 7 (d) 3² × 7
  5. 5.How many prime numbers are there between 70 and 80? (a) 2 (b) 4 (c) 3 (d) 5
  6. 6.How many prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 9 (d) 7
  7. 7.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2² × 7 (d) 2³ × 7
  8. 8.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 8 (d) 7
  9. 9.How many factors does 22 have? (a) 4 (b) 3 (c) 2 (d) 5
  10. 10.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
  11. 11.What is the prime factorisation of 35? (a) 5 × 7² (b) 5 × 7 (c) 5² × 7 (d) 5³ × 7
  12. 12.How many factors does 57 have? (a) 4 (b) 2 (c) 5 (d) 3
  13. 13.How many prime numbers are there between 40 and 60? (a) 6 (b) 4 (c) 7 (d) 5
  14. 14.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  15. 15.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
  16. 16.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2³ × 3
  17. 17.How many factors does 32 have? (a) 7 (b) 4 (c) 6 (d) 5
  18. 18.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 11 (d) 1
  19. 19.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
  20. 20.How many factors does 25 have? (a) 4 (b) 1 (c) 2 (d) 3
  21. 21.How many factors does 74 have? (a) 4 (b) 2 (c) 3 (d) 5
  22. 22.How many factors does 34 have? (a) 5 (b) 3 (c) 4 (d) 2
  23. 23.What is the prime factorisation of 63? (a) 3² × 7 (b) 3 × 7 (c) 3³ × 7 (d) 3 × 7²
  24. 24.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  25. 25.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
  26. 26.What is the smallest prime factor of 247? (a) 19 (b) 1 (c) 2 (d) 13
  27. 27.How many factors does 110 have? (a) 8 (b) 6 (c) 9 (d) 7
  28. 28.What is the smallest prime factor of 403? (a) 13 (b) 31 (c) 2 (d) 1
  29. 29.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  30. 30.How many prime numbers are there between 40 and 50? (a) 2 (b) 3 (c) 5 (d) 4
  31. 31.What is the smallest prime factor of 133? (a) 7 (b) 19 (c) 2 (d) 1
  32. 32.What is the smallest prime factor of 119? (a) 17 (b) 2 (c) 1 (d) 7
  33. 33.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 2 (d) 1
  34. 34.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
  35. 35.What is the smallest prime factor of 169? (a) 1 (b) 13 (c) 3 (d) 2
  36. 36.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 1 (d) 3
  37. 37.How many factors does 65 have? (a) 2 (b) 3 (c) 4 (d) 5
  38. 38.What is the smallest prime factor of 319? (a) 11 (b) 29 (c) 1 (d) 2
  39. 39.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁴ × 3 × 7 (d) 2⁵ × 3 × 7
  40. 40.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2² × 3 × 5

Answer key

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

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