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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 28 · 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 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
  2. 2.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 5 (d) 4
  3. 3.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2³ × 5 (d) 2² × 5
  4. 4.What is the smallest prime factor of 57? (a) 3 (b) 19 (c) 2 (d) 1
  5. 5.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 1 (d) 11
  6. 6.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 2 (d) 1
  7. 7.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2 × 3² (c) 2² × 3 (d) 2² × 3²
  8. 8.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 2 (d) 1
  9. 9.How many prime numbers are there between 80 and 100? (a) 5 (b) 4 (c) 3 (d) 2
  10. 10.How many factors does 74 have? (a) 5 (b) 2 (c) 4 (d) 3
  11. 11.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 1 (d) 4
  12. 12.What is the smallest prime factor of 69? (a) 1 (b) 23 (c) 2 (d) 3
  13. 13.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  14. 14.What is the prime factorisation of 360? (a) 2³ × 3² × 5 (b) 2 × 3² × 5³ (c) 2⁴ × 3² × 5 (d) 2² × 3² × 5
  15. 15.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 6 (d) 5
  16. 16.How many factors does 45 have? (a) 7 (b) 4 (c) 6 (d) 5
  17. 17.What is the smallest prime factor of 21? (a) 3 (b) 1 (c) 7 (d) 2
  18. 18.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 13 (d) 2
  19. 19.What is the smallest prime factor of 341? (a) 31 (b) 2 (c) 1 (d) 11
  20. 20.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 6 (d) 8
  21. 21.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  22. 22.How many factors does 75 have? (a) 7 (b) 6 (c) 5 (d) 4
  23. 23.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 4 (d) 3
  24. 24.What is the smallest prime factor of 377? (a) 13 (b) 29 (c) 1 (d) 2
  25. 25.How many factors does 55 have? (a) 2 (b) 4 (c) 5 (d) 3
  26. 26.How many factors does 90 have? (a) 11 (b) 10 (c) 13 (d) 12
  27. 27.How many factors does 40 have? (a) 9 (b) 7 (c) 8 (d) 6
  28. 28.What is the prime factorisation of 12? (a) 2 × 3² (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3
  29. 29.How many factors does 112 have? (a) 8 (b) 9 (c) 11 (d) 10
  30. 30.How many factors does 16 have? (a) 3 (b) 4 (c) 6 (d) 5
  31. 31.How many prime numbers are there between 50 and 60? (a) 4 (b) 3 (c) 2 (d) 1
  32. 32.How many factors does 66 have? (a) 8 (b) 9 (c) 6 (d) 7
  33. 33.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 4 (d) 5
  34. 34.What is the smallest prime factor of 217? (a) 31 (b) 1 (c) 2 (d) 7
  35. 35.How many factors does 17 have? (a) 1 (b) 3 (c) 2 (d) 4
  36. 36.How many factors does 41 have? (a) 1 (b) 3 (c) 2 (d) 4
  37. 37.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7 (c) 2² × 7 (d) 2 × 7²
  38. 38.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 7 (d) 6
  39. 39.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 3 (d) 29
  40. 40.How many factors does 86 have? (a) 3 (b) 4 (c) 2 (d) 5

Answer key

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

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