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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 72 · 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 40 and 50? (a) 2 (b) 5 (c) 4 (d) 3
  2. 2.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 8 (d) 9
  3. 3.How many factors does 63 have? (a) 5 (b) 6 (c) 4 (d) 7
  4. 4.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2² × 3²
  5. 5.How many factors does 38 have? (a) 3 (b) 2 (c) 5 (d) 4
  6. 6.How many prime numbers are there between 60 and 90? (a) 8 (b) 9 (c) 7 (d) 6
  7. 7.How many factors does 116 have? (a) 5 (b) 4 (c) 7 (d) 6
  8. 8.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7² (d) 5 × 7
  9. 9.How many prime numbers are there between 80 and 90? (a) 3 (b) 4 (c) 2 (d) 1
  10. 10.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 2 (d) 1
  11. 11.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2 × 3 × 7³ (d) 2³ × 3 × 7
  12. 12.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  13. 13.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  14. 14.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 5 (d) 6
  15. 15.How many factors does 80 have? (a) 8 (b) 9 (c) 11 (d) 10
  16. 16.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 7 (d) 6
  17. 17.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2⁴ × 5 (c) 2² × 5 (d) 2 × 5³
  18. 18.How many factors does 43 have? (a) 3 (b) 4 (c) 2 (d) 1
  19. 19.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
  20. 20.How many factors does 102 have? (a) 9 (b) 8 (c) 6 (d) 7
  21. 21.What is the prime factorisation of 28? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  22. 22.What is the prime factorisation of 21? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
  23. 23.How many factors does 107 have? (a) 2 (b) 3 (c) 1 (d) 4
  24. 24.How many factors does 30 have? (a) 9 (b) 8 (c) 6 (d) 7
  25. 25.What is the smallest prime factor of 119? (a) 1 (b) 2 (c) 7 (d) 17
  26. 26.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  27. 27.How many factors does 94 have? (a) 3 (b) 2 (c) 4 (d) 5
  28. 28.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 8 (d) 7
  29. 29.How many factors does 52 have? (a) 6 (b) 7 (c) 5 (d) 4
  30. 30.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 2 (d) 1
  31. 31.How many factors does 109 have? (a) 2 (b) 3 (c) 4 (d) 1
  32. 32.How many factors does 50 have? (a) 5 (b) 6 (c) 7 (d) 4
  33. 33.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 1 (d) 2
  34. 34.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 2 (d) 1
  35. 35.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2³ × 3²
  36. 36.How many factors does 39 have? (a) 4 (b) 5 (c) 3 (d) 2
  37. 37.What is the smallest prime factor of 161? (a) 2 (b) 7 (c) 1 (d) 23
  38. 38.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 6 (d) 9
  39. 39.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
  40. 40.What is the smallest prime factor of 39? (a) 3 (b) 2 (c) 1 (d) 13

Answer key

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

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