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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 75 · 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 30 have? (a) 6 (b) 9 (c) 8 (d) 7
  2. 2.What is the smallest prime factor of 69? (a) 23 (b) 3 (c) 2 (d) 1
  3. 3.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 5 (d) 2
  4. 4.How many factors does 27 have? (a) 4 (b) 5 (c) 3 (d) 2
  5. 5.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
  6. 6.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 2 (d) 1
  7. 7.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5²
  8. 8.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 1 (d) 11
  9. 9.How many factors does 46 have? (a) 2 (b) 5 (c) 4 (d) 3
  10. 10.How many factors does 59 have? (a) 4 (b) 1 (c) 3 (d) 2
  11. 11.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2² × 5 × 7
  12. 12.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
  13. 13.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  14. 14.How many factors does 77 have? (a) 4 (b) 2 (c) 5 (d) 3
  15. 15.How many factors does 94 have? (a) 4 (b) 3 (c) 5 (d) 2
  16. 16.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  17. 17.How many factors does 114 have? (a) 8 (b) 6 (c) 7 (d) 9
  18. 18.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 1 (d) 2
  19. 19.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  20. 20.How many prime numbers are there between 50 and 70? (a) 6 (b) 5 (c) 3 (d) 4
  21. 21.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 4 (d) 6
  22. 22.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
  23. 23.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 3 (d) 0
  24. 24.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2 × 5 × 7⁴
  25. 25.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  26. 26.How many factors does 62 have? (a) 3 (b) 4 (c) 5 (d) 2
  27. 27.How many prime numbers are there between 30 and 60? (a) 6 (b) 9 (c) 8 (d) 7
  28. 28.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
  29. 29.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
  30. 30.How many factors does 56 have? (a) 7 (b) 9 (c) 8 (d) 6
  31. 31.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2 × 5³ (c) 2² × 5 (d) 2³ × 5
  32. 32.How many factors does 97 have? (a) 4 (b) 1 (c) 2 (d) 3
  33. 33.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 7 (d) 1
  34. 34.How many prime numbers are there between 70 and 100? (a) 5 (b) 6 (c) 8 (d) 7
  35. 35.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2⁴ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7³
  36. 36.What is the smallest prime factor of 21? (a) 2 (b) 7 (c) 1 (d) 3
  37. 37.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
  38. 38.How many factors does 35 have? (a) 3 (b) 5 (c) 2 (d) 4
  39. 39.How many factors does 36 have? (a) 10 (b) 7 (c) 8 (d) 9
  40. 40.How many factors does 93 have? (a) 4 (b) 3 (c) 5 (d) 2

Answer key

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

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