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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 70 · 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 prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 9 (d) 7
  2. 2.How many prime numbers are there between 10 and 40? (a) 10 (b) 9 (c) 8 (d) 7
  3. 3.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 11 (d) 7
  4. 4.How many factors does 20 have? (a) 4 (b) 6 (c) 7 (d) 5
  5. 5.How many factors does 33 have? (a) 3 (b) 5 (c) 4 (d) 2
  6. 6.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7²
  7. 7.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  8. 8.What is the smallest prime factor of 221? (a) 2 (b) 1 (c) 13 (d) 17
  9. 9.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  10. 10.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 4 (d) 6
  11. 11.How many prime numbers are there between 40 and 60? (a) 5 (b) 6 (c) 7 (d) 4
  12. 12.What is the smallest prime factor of 209? (a) 2 (b) 1 (c) 11 (d) 19
  13. 13.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 8 (d) 5
  14. 14.How many factors does 99 have? (a) 7 (b) 5 (c) 6 (d) 4
  15. 15.How many factors does 101 have? (a) 1 (b) 4 (c) 3 (d) 2
  16. 16.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2 × 3² (c) 2² × 3³ (d) 2² × 3²
  17. 17.How many prime numbers are there between 90 and 100? (a) 1 (b) 0 (c) 3 (d) 2
  18. 18.How many prime numbers are there between 90 and 110? (a) 6 (b) 7 (c) 4 (d) 5
  19. 19.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  20. 20.What is the smallest prime factor of 49? (a) 1 (b) 2 (c) 7 (d) 3
  21. 21.How many factors does 49 have? (a) 2 (b) 4 (c) 1 (d) 3
  22. 22.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 2 (d) 4
  23. 23.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2³ × 5
  24. 24.What is the smallest prime factor of 145? (a) 1 (b) 5 (c) 29 (d) 2
  25. 25.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 4 (d) 5
  26. 26.How many prime numbers are there between 30 and 50? (a) 7 (b) 4 (c) 6 (d) 5
  27. 27.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
  28. 28.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 7 (d) 1
  29. 29.How many factors does 114 have? (a) 9 (b) 7 (c) 8 (d) 6
  30. 30.How many prime numbers are there between 50 and 80? (a) 7 (b) 9 (c) 6 (d) 8
  31. 31.How many factors does 94 have? (a) 2 (b) 3 (c) 4 (d) 5
  32. 32.What is the smallest prime factor of 57? (a) 19 (b) 1 (c) 2 (d) 3
  33. 33.How many factors does 35 have? (a) 5 (b) 4 (c) 3 (d) 2
  34. 34.How many factors does 26 have? (a) 5 (b) 4 (c) 3 (d) 2
  35. 35.What is the smallest prime factor of 39? (a) 3 (b) 2 (c) 13 (d) 1
  36. 36.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2² × 7 (d) 2³ × 7
  37. 37.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  38. 38.What is the prime factorisation of 21? (a) 3 × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3² × 7
  39. 39.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 8 (d) 6
  40. 40.How many factors does 93 have? (a) 3 (b) 4 (c) 2 (d) 5

Answer key

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

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