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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 20 · 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) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
  2. 2.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7
  3. 3.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 8 (d) 6
  4. 4.How many prime numbers are there between 30 and 50? (a) 5 (b) 6 (c) 4 (d) 7
  5. 5.How many factors does 84 have? (a) 12 (b) 13 (c) 10 (d) 11
  6. 6.How many factors does 49 have? (a) 3 (b) 4 (c) 2 (d) 1
  7. 7.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 2 (d) 3
  8. 8.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7³
  9. 9.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  10. 10.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 4 (d) 2
  11. 11.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2³ × 3 (d) 2⁴ × 3
  12. 12.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 6 (d) 9
  13. 13.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
  14. 14.How many factors does 23 have? (a) 3 (b) 2 (c) 4 (d) 1
  15. 15.How many factors does 48 have? (a) 9 (b) 10 (c) 11 (d) 8
  16. 16.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 7 (d) 1
  17. 17.How many factors does 95 have? (a) 2 (b) 3 (c) 4 (d) 5
  18. 18.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
  19. 19.What is the smallest prime factor of 253? (a) 23 (b) 2 (c) 11 (d) 1
  20. 20.How many factors does 66 have? (a) 7 (b) 6 (c) 9 (d) 8
  21. 21.How many factors does 46 have? (a) 3 (b) 2 (c) 5 (d) 4
  22. 22.How many factors does 91 have? (a) 5 (b) 2 (c) 4 (d) 3
  23. 23.How many factors does 43 have? (a) 2 (b) 1 (c) 3 (d) 4
  24. 24.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2 × 3² (d) 2² × 3²
  25. 25.How many factors does 17 have? (a) 4 (b) 1 (c) 3 (d) 2
  26. 26.How many prime numbers are there between 20 and 40? (a) 4 (b) 3 (c) 5 (d) 6
  27. 27.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2⁴ × 3 × 5
  28. 28.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7 (c) 2² × 7 (d) 2 × 7²
  29. 29.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
  30. 30.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 5 (d) 6
  31. 31.What is the smallest prime factor of 55? (a) 11 (b) 2 (c) 5 (d) 1
  32. 32.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2
  33. 33.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 3 (d) 4
  34. 34.How many factors does 69 have? (a) 5 (b) 2 (c) 4 (d) 3
  35. 35.What is the prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7
  36. 36.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  37. 37.How many factors does 55 have? (a) 2 (b) 3 (c) 4 (d) 5
  38. 38.How many factors does 37 have? (a) 3 (b) 4 (c) 2 (d) 1
  39. 39.How many factors does 67 have? (a) 4 (b) 1 (c) 3 (d) 2
  40. 40.What is the smallest prime factor of 119? (a) 7 (b) 1 (c) 2 (d) 17

Answer key

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

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