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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 58 · 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 factors does 75 have? (a) 6 (b) 4 (c) 5 (d) 7
  2. 2.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 9 (d) 6
  3. 3.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
  4. 4.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 4 (d) 6
  5. 5.How many prime numbers are there between 30 and 60? (a) 9 (b) 8 (c) 7 (d) 6
  6. 6.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
  7. 7.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2³ × 3 × 7 (d) 2² × 3 × 7
  8. 8.What is the prime factorisation of 24? (a) 2² × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3³
  9. 9.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 3 (d) 2
  10. 10.How many factors does 66 have? (a) 9 (b) 7 (c) 6 (d) 8
  11. 11.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 6 (d) 5
  12. 12.How many prime numbers are there between 20 and 50? (a) 6 (b) 9 (c) 7 (d) 8
  13. 13.How many factors does 89 have? (a) 3 (b) 4 (c) 1 (d) 2
  14. 14.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 1 (d) 4
  15. 15.How many factors does 110 have? (a) 6 (b) 7 (c) 9 (d) 8
  16. 16.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2⁴ × 3² (c) 2³ × 3² (d) 2² × 3²
  17. 17.How many prime numbers are there between 90 and 120? (a) 5 (b) 6 (c) 8 (d) 7
  18. 18.How many factors does 40 have? (a) 7 (b) 6 (c) 9 (d) 8
  19. 19.How many prime numbers are there between 10 and 40? (a) 9 (b) 8 (c) 7 (d) 10
  20. 20.What is the smallest prime factor of 161? (a) 23 (b) 2 (c) 7 (d) 1
  21. 21.What is the smallest prime factor of 119? (a) 7 (b) 2 (c) 1 (d) 17
  22. 22.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2² × 3² × 7
  23. 23.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
  24. 24.How many factors does 93 have? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 1 (d) 4
  26. 26.What is the smallest prime factor of 133? (a) 1 (b) 19 (c) 2 (d) 7
  27. 27.How many factors does 102 have? (a) 8 (b) 9 (c) 6 (d) 7
  28. 28.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 2 (d) 5
  29. 29.How many factors does 115 have? (a) 2 (b) 4 (c) 5 (d) 3
  30. 30.How many factors does 51 have? (a) 3 (b) 5 (c) 2 (d) 4
  31. 31.How many factors does 30 have? (a) 7 (b) 9 (c) 8 (d) 6
  32. 32.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 4 (d) 3
  33. 33.How many factors does 69 have? (a) 5 (b) 2 (c) 3 (d) 4
  34. 34.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2 × 5³ (c) 2³ × 5 (d) 2² × 5
  35. 35.What is the smallest prime factor of 319? (a) 1 (b) 29 (c) 11 (d) 2
  36. 36.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 4 (d) 2
  37. 37.How many factors does 50 have? (a) 4 (b) 7 (c) 6 (d) 5
  38. 38.How many factors does 42 have? (a) 8 (b) 9 (c) 6 (d) 7
  39. 39.How many prime numbers are there between 90 and 110? (a) 5 (b) 6 (c) 7 (d) 4
  40. 40.What is the smallest prime factor of 377? (a) 13 (b) 2 (c) 29 (d) 1

Answer key

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

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