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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 166 · 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 91? (a) 13 (b) 2 (c) 1 (d) 7
  2. 2.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7² (d) 3 × 7
  3. 3.How many factors does 38 have? (a) 5 (b) 3 (c) 4 (d) 2
  4. 4.How many factors does 76 have? (a) 7 (b) 5 (c) 4 (d) 6
  5. 5.What is the smallest prime factor of 299? (a) 1 (b) 2 (c) 23 (d) 13
  6. 6.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 8 (d) 9
  7. 7.How many prime numbers are there between 50 and 60? (a) 3 (b) 4 (c) 2 (d) 1
  8. 8.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 4 (d) 5
  9. 9.What is the smallest prime factor of 57? (a) 3 (b) 2 (c) 19 (d) 1
  10. 10.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  11. 11.How many factors does 37 have? (a) 3 (b) 1 (c) 4 (d) 2
  12. 12.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 7 (d) 5
  13. 13.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 7 (d) 3
  14. 14.How many factors does 93 have? (a) 3 (b) 2 (c) 4 (d) 5
  15. 15.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3³
  16. 16.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  17. 17.How many factors does 51 have? (a) 5 (b) 4 (c) 3 (d) 2
  18. 18.How many factors does 111 have? (a) 2 (b) 3 (c) 4 (d) 5
  19. 19.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 9 (d) 7
  20. 20.How many factors does 107 have? (a) 1 (b) 4 (c) 2 (d) 3
  21. 21.How many factors does 22 have? (a) 3 (b) 2 (c) 5 (d) 4
  22. 22.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
  23. 23.How many factors does 30 have? (a) 6 (b) 9 (c) 7 (d) 8
  24. 24.How many factors does 70 have? (a) 7 (b) 8 (c) 6 (d) 9
  25. 25.How many prime numbers are there between 60 and 70? (a) 4 (b) 2 (c) 1 (d) 3
  26. 26.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7²
  27. 27.What is the smallest prime factor of 187? (a) 1 (b) 11 (c) 2 (d) 17
  28. 28.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3³ (c) 2 × 3² (d) 2² × 3²
  29. 29.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  30. 30.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 4 (d) 6
  31. 31.How many factors does 58 have? (a) 5 (b) 3 (c) 2 (d) 4
  32. 32.What is the smallest prime factor of 247? (a) 19 (b) 1 (c) 2 (d) 13
  33. 33.How many factors does 63 have? (a) 4 (b) 5 (c) 7 (d) 6
  34. 34.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2 × 5 (d) 2³ × 5
  35. 35.How many factors does 43 have? (a) 3 (b) 4 (c) 1 (d) 2
  36. 36.How many factors does 36 have? (a) 7 (b) 10 (c) 8 (d) 9
  37. 37.How many factors does 54 have? (a) 7 (b) 6 (c) 9 (d) 8
  38. 38.What is the smallest prime factor of 93? (a) 1 (b) 31 (c) 2 (d) 3
  39. 39.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7²
  40. 40.What is the smallest prime factor of 217? (a) 31 (b) 2 (c) 1 (d) 7

Answer key

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

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