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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 71 · 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 85? (a) 5 (b) 1 (c) 17 (d) 2
  2. 2.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7 (c) 3 × 7² (d) 3³ × 7
  3. 3.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  4. 4.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
  5. 5.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 2 (d) 3
  6. 6.What is the smallest prime factor of 115? (a) 2 (b) 1 (c) 5 (d) 23
  7. 7.What is the smallest prime factor of 39? (a) 13 (b) 1 (c) 2 (d) 3
  8. 8.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7
  9. 9.How many factors does 117 have? (a) 5 (b) 4 (c) 7 (d) 6
  10. 10.How many factors does 66 have? (a) 8 (b) 7 (c) 6 (d) 9
  11. 11.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2
  12. 12.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5² (c) 2² × 5 (d) 2 × 5
  13. 13.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
  14. 14.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 7 (d) 2
  15. 15.How many factors does 30 have? (a) 6 (b) 7 (c) 8 (d) 9
  16. 16.What is the smallest prime factor of 57? (a) 1 (b) 3 (c) 19 (d) 2
  17. 17.What is the prime factorisation of 18? (a) 2 × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2² × 3²
  18. 18.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2³ × 3
  19. 19.How many prime numbers are there between 30 and 60? (a) 9 (b) 7 (c) 8 (d) 6
  20. 20.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 10 (d) 7
  21. 21.How many factors does 99 have? (a) 4 (b) 5 (c) 7 (d) 6
  22. 22.How many factors does 61 have? (a) 3 (b) 4 (c) 1 (d) 2
  23. 23.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
  24. 24.How many factors does 71 have? (a) 1 (b) 3 (c) 4 (d) 2
  25. 25.What is the smallest prime factor of 203? (a) 2 (b) 7 (c) 1 (d) 29
  26. 26.How many factors does 83 have? (a) 3 (b) 4 (c) 1 (d) 2
  27. 27.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 6 (d) 3
  28. 28.How many prime numbers are there between 60 and 90? (a) 6 (b) 9 (c) 7 (d) 8
  29. 29.How many factors does 85 have? (a) 4 (b) 3 (c) 2 (d) 5
  30. 30.What is the smallest prime factor of 145? (a) 29 (b) 5 (c) 2 (d) 1
  31. 31.How many prime numbers are there between 10 and 30? (a) 6 (b) 5 (c) 8 (d) 7
  32. 32.What is the smallest prime factor of 119? (a) 17 (b) 2 (c) 1 (d) 7
  33. 33.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7³
  34. 34.How many factors does 75 have? (a) 6 (b) 7 (c) 4 (d) 5
  35. 35.How many factors does 97 have? (a) 4 (b) 3 (c) 1 (d) 2
  36. 36.How many factors does 29 have? (a) 3 (b) 2 (c) 1 (d) 4
  37. 37.How many factors does 86 have? (a) 5 (b) 2 (c) 4 (d) 3
  38. 38.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 1 (d) 7
  39. 39.What is the smallest prime factor of 187? (a) 2 (b) 11 (c) 17 (d) 1
  40. 40.How many factors does 101 have? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

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

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