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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 44 · 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 20 have? (a) 4 (b) 7 (c) 5 (d) 6
  2. 2.How many factors does 63 have? (a) 7 (b) 5 (c) 6 (d) 4
  3. 3.How many factors does 23 have? (a) 4 (b) 1 (c) 2 (d) 3
  4. 4.How many factors does 89 have? (a) 1 (b) 4 (c) 2 (d) 3
  5. 5.How many factors does 32 have? (a) 7 (b) 4 (c) 6 (d) 5
  6. 6.How many factors does 67 have? (a) 3 (b) 2 (c) 1 (d) 4
  7. 7.How many factors does 101 have? (a) 4 (b) 3 (c) 2 (d) 1
  8. 8.What is the smallest prime factor of 253? (a) 11 (b) 23 (c) 2 (d) 1
  9. 9.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2² × 5
  10. 10.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 5 (d) 3
  11. 11.How many prime numbers are there between 40 and 50? (a) 2 (b) 3 (c) 5 (d) 4
  12. 12.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  13. 13.How many prime numbers are there between 20 and 50? (a) 7 (b) 9 (c) 8 (d) 6
  14. 14.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 4 (d) 6
  15. 15.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 2 (d) 1
  16. 16.What is the smallest prime factor of 85? (a) 17 (b) 2 (c) 5 (d) 1
  17. 17.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2² × 5 (d) 2³ × 5
  18. 18.What is the prime factorisation of 63? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
  19. 19.How many factors does 30 have? (a) 8 (b) 9 (c) 7 (d) 6
  20. 20.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  21. 21.How many prime numbers are there between 80 and 90? (a) 4 (b) 2 (c) 3 (d) 1
  22. 22.How many factors does 12 have? (a) 7 (b) 6 (c) 5 (d) 4
  23. 23.How many factors does 118 have? (a) 4 (b) 5 (c) 3 (d) 2
  24. 24.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁵ × 3 (d) 2⁴ × 3
  25. 25.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
  26. 26.How many factors does 34 have? (a) 3 (b) 5 (c) 4 (d) 2
  27. 27.How many factors does 24 have? (a) 8 (b) 6 (c) 9 (d) 7
  28. 28.What is the smallest prime factor of 403? (a) 2 (b) 31 (c) 13 (d) 1
  29. 29.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  30. 30.How many factors does 52 have? (a) 6 (b) 7 (c) 4 (d) 5
  31. 31.How many factors does 65 have? (a) 3 (b) 4 (c) 2 (d) 5
  32. 32.How many factors does 56 have? (a) 7 (b) 9 (c) 8 (d) 6
  33. 33.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 7 (d) 9
  34. 34.What is the prime factorisation of 45? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
  35. 35.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
  36. 36.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 6 (d) 5
  37. 37.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3²
  38. 38.What is the prime factorisation of 21? (a) 3 × 7 (b) 3² × 7 (c) 3 × 7² (d) 3³ × 7
  39. 39.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  40. 40.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5

Answer key

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

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