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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 97 · 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 prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  2. 2.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3 (d) 2 × 3²
  3. 3.What is the smallest prime factor of 155? (a) 31 (b) 1 (c) 5 (d) 2
  4. 4.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 9 (d) 7
  5. 5.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 1 (d) 0
  6. 6.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7 (c) 3² × 7 (d) 3 × 7²
  7. 7.What is the smallest prime factor of 49? (a) 3 (b) 7 (c) 1 (d) 2
  8. 8.How many factors does 86 have? (a) 5 (b) 2 (c) 4 (d) 3
  9. 9.How many factors does 30 have? (a) 6 (b) 9 (c) 8 (d) 7
  10. 10.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 1 (d) 5
  11. 11.How many factors does 93 have? (a) 4 (b) 3 (c) 5 (d) 2
  12. 12.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7³ (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  13. 13.How many prime numbers are there between 10 and 30? (a) 6 (b) 7 (c) 8 (d) 5
  14. 14.How many factors does 107 have? (a) 4 (b) 2 (c) 1 (d) 3
  15. 15.How many prime numbers are there between 80 and 110? (a) 7 (b) 9 (c) 6 (d) 8
  16. 16.How many factors does 53 have? (a) 3 (b) 1 (c) 4 (d) 2
  17. 17.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3 (c) 2² × 3² (d) 2 × 3²
  18. 18.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 3 (d) 4
  19. 19.What is the prime factorisation of 24? (a) 2² × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3³
  20. 20.What is the prime factorisation of 15? (a) 3 × 5² (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5
  21. 21.What is the smallest prime factor of 65? (a) 2 (b) 5 (c) 1 (d) 13
  22. 22.What is the smallest prime factor of 39? (a) 13 (b) 1 (c) 3 (d) 2
  23. 23.How many prime numbers are there between 70 and 100? (a) 5 (b) 7 (c) 6 (d) 8
  24. 24.How many factors does 44 have? (a) 4 (b) 7 (c) 5 (d) 6
  25. 25.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 1 (d) 2
  26. 26.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2² × 3 × 5 × 7
  27. 27.What is the smallest prime factor of 403? (a) 1 (b) 2 (c) 13 (d) 31
  28. 28.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 6 (d) 8
  29. 29.How many factors does 33 have? (a) 3 (b) 2 (c) 4 (d) 5
  30. 30.How many factors does 65 have? (a) 5 (b) 3 (c) 2 (d) 4
  31. 31.How many factors does 38 have? (a) 2 (b) 5 (c) 4 (d) 3
  32. 32.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 1 (d) 3
  33. 33.How many factors does 58 have? (a) 4 (b) 3 (c) 2 (d) 5
  34. 34.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 1 (d) 4
  35. 35.What is the smallest prime factor of 35? (a) 1 (b) 2 (c) 5 (d) 7
  36. 36.How many factors does 52 have? (a) 4 (b) 6 (c) 5 (d) 7
  37. 37.How many factors does 100 have? (a) 9 (b) 10 (c) 7 (d) 8
  38. 38.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  39. 39.What is the smallest prime factor of 169? (a) 2 (b) 1 (c) 13 (d) 3
  40. 40.How many factors does 101 have? (a) 4 (b) 3 (c) 1 (d) 2

Answer key

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

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