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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 12 · 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 17 have? (a) 2 (b) 4 (c) 3 (d) 1
  2. 2.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3² × 5 (c) 3 × 5² (d) 3 × 5
  3. 3.How many prime numbers are there between 80 and 110? (a) 7 (b) 6 (c) 9 (d) 8
  4. 4.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 2 (d) 1
  5. 5.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2⁵ × 3 (d) 2³ × 3
  6. 6.How many factors does 107 have? (a) 2 (b) 1 (c) 4 (d) 3
  7. 7.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 2 (d) 3
  8. 8.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  9. 9.How many factors does 101 have? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.What is the smallest prime factor of 203? (a) 7 (b) 2 (c) 1 (d) 29
  11. 11.How many factors does 46 have? (a) 2 (b) 3 (c) 4 (d) 5
  12. 12.How many factors does 29 have? (a) 3 (b) 2 (c) 4 (d) 1
  13. 13.What is the smallest prime factor of 55? (a) 11 (b) 1 (c) 2 (d) 5
  14. 14.What is the smallest prime factor of 319? (a) 11 (b) 1 (c) 2 (d) 29
  15. 15.How many factors does 40 have? (a) 6 (b) 7 (c) 9 (d) 8
  16. 16.How many prime numbers are there between 10 and 40? (a) 8 (b) 10 (c) 9 (d) 7
  17. 17.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  18. 18.How many factors does 22 have? (a) 3 (b) 5 (c) 2 (d) 4
  19. 19.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
  20. 20.How many factors does 20 have? (a) 7 (b) 6 (c) 5 (d) 4
  21. 21.What is the smallest prime factor of 145? (a) 5 (b) 29 (c) 2 (d) 1
  22. 22.How many factors does 82 have? (a) 5 (b) 3 (c) 2 (d) 4
  23. 23.How many factors does 110 have? (a) 7 (b) 9 (c) 6 (d) 8
  24. 24.How many factors does 72 have? (a) 10 (b) 11 (c) 13 (d) 12
  25. 25.How many factors does 105 have? (a) 7 (b) 9 (c) 6 (d) 8
  26. 26.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 2 (d) 7
  27. 27.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  28. 28.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 4 (d) 2
  29. 29.How many factors does 68 have? (a) 6 (b) 7 (c) 4 (d) 5
  30. 30.How many prime numbers are there between 70 and 80? (a) 5 (b) 4 (c) 2 (d) 3
  31. 31.How many factors does 119 have? (a) 2 (b) 5 (c) 3 (d) 4
  32. 32.How many factors does 34 have? (a) 5 (b) 2 (c) 3 (d) 4
  33. 33.What is the smallest prime factor of 209? (a) 1 (b) 11 (c) 19 (d) 2
  34. 34.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
  35. 35.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 3 (d) 2
  36. 36.How many factors does 24 have? (a) 7 (b) 6 (c) 8 (d) 9
  37. 37.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2² × 5 × 7
  38. 38.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 7 (d) 2
  39. 39.What is the smallest prime factor of 221? (a) 1 (b) 2 (c) 17 (d) 13
  40. 40.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2⁴ × 3 (d) 2³ × 3

Answer key

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

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