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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 151 · 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 smallest prime factor of 65? (a) 5 (b) 1 (c) 2 (d) 13
  2. 2.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2⁴ × 3 (c) 2² × 3 (d) 2³ × 3
  3. 3.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 1 (d) 3
  4. 4.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 5 (d) 4
  5. 5.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  6. 6.How many factors does 64 have? (a) 6 (b) 8 (c) 5 (d) 7
  7. 7.How many factors does 49 have? (a) 2 (b) 1 (c) 4 (d) 3
  8. 8.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 1 (d) 3
  9. 9.What is the smallest prime factor of 93? (a) 2 (b) 1 (c) 3 (d) 31
  10. 10.How many factors does 113 have? (a) 1 (b) 3 (c) 2 (d) 4
  11. 11.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 2 (d) 7
  12. 12.What is the prime factorisation of 12? (a) 2² × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2 × 3
  13. 13.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13
  14. 14.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  15. 15.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 4 (d) 6
  16. 16.How many prime numbers are there between 70 and 90? (a) 6 (b) 7 (c) 4 (d) 5
  17. 17.How many factors does 89 have? (a) 2 (b) 1 (c) 4 (d) 3
  18. 18.How many factors does 82 have? (a) 5 (b) 2 (c) 4 (d) 3
  19. 19.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 3 (d) 2
  20. 20.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
  21. 21.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 6 (d) 7
  22. 22.How many factors does 38 have? (a) 3 (b) 2 (c) 5 (d) 4
  23. 23.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 9 (d) 8
  24. 24.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 5 (d) 6
  25. 25.How many factors does 51 have? (a) 5 (b) 3 (c) 4 (d) 2
  26. 26.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 4 (d) 3
  27. 27.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3²
  28. 28.How many factors does 75 have? (a) 6 (b) 5 (c) 7 (d) 4
  29. 29.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
  30. 30.How many factors does 19 have? (a) 2 (b) 3 (c) 4 (d) 1
  31. 31.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 3 (d) 4
  32. 32.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  33. 33.How many factors does 31 have? (a) 3 (b) 1 (c) 4 (d) 2
  34. 34.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  35. 35.What is the smallest prime factor of 187? (a) 11 (b) 2 (c) 1 (d) 17
  36. 36.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 2 (d) 1
  37. 37.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  38. 38.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 7 (d) 1
  39. 39.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
  40. 40.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7

Answer key

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

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