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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 116 · 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 40? (a) 2² × 5 (b) 2⁴ × 5 (c) 2³ × 5 (d) 2 × 5³
  2. 2.What is the smallest prime factor of 121? (a) 2 (b) 3 (c) 1 (d) 11
  3. 3.What is the smallest prime factor of 51? (a) 2 (b) 17 (c) 3 (d) 1
  4. 4.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7 (d) 5 × 7²
  5. 5.How many factors does 88 have? (a) 6 (b) 7 (c) 9 (d) 8
  6. 6.How many factors does 85 have? (a) 2 (b) 4 (c) 3 (d) 5
  7. 7.What is the smallest prime factor of 35? (a) 2 (b) 1 (c) 5 (d) 7
  8. 8.How many factors does 90 have? (a) 10 (b) 12 (c) 11 (d) 13
  9. 9.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  10. 10.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁵ × 3² (d) 2⁴ × 3²
  11. 11.What is the smallest prime factor of 21? (a) 7 (b) 3 (c) 2 (d) 1
  12. 12.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  13. 13.How many prime numbers are there between 40 and 60? (a) 7 (b) 5 (c) 4 (d) 6
  14. 14.How many factors does 54 have? (a) 6 (b) 9 (c) 8 (d) 7
  15. 15.How many factors does 28 have? (a) 5 (b) 4 (c) 6 (d) 7
  16. 16.How many factors does 38 have? (a) 2 (b) 4 (c) 3 (d) 5
  17. 17.How many prime numbers are there between 80 and 110? (a) 9 (b) 8 (c) 6 (d) 7
  18. 18.How many prime numbers are there between 60 and 70? (a) 4 (b) 2 (c) 3 (d) 1
  19. 19.What is the prime factorisation of 12? (a) 2 × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3²
  20. 20.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
  21. 21.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2⁵ × 7 (d) 2 × 7⁴
  22. 22.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2
  23. 23.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
  24. 24.What is the prime factorisation of 15? (a) 3 × 5² (b) 3 × 5 (c) 3³ × 5 (d) 3² × 5
  25. 25.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  26. 26.What is the smallest prime factor of 49? (a) 1 (b) 2 (c) 3 (d) 7
  27. 27.How many factors does 118 have? (a) 4 (b) 5 (c) 3 (d) 2
  28. 28.What is the smallest prime factor of 169? (a) 13 (b) 1 (c) 3 (d) 2
  29. 29.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 11 (d) 5
  30. 30.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2⁴ × 5 × 7
  31. 31.How many prime numbers are there between 40 and 70? (a) 6 (b) 9 (c) 7 (d) 8
  32. 32.What is the smallest prime factor of 69? (a) 3 (b) 1 (c) 23 (d) 2
  33. 33.How many prime numbers are there between 40 and 50? (a) 2 (b) 5 (c) 4 (d) 3
  34. 34.How many factors does 99 have? (a) 6 (b) 5 (c) 4 (d) 7
  35. 35.How many factors does 44 have? (a) 6 (b) 5 (c) 7 (d) 4
  36. 36.What is the smallest prime factor of 209? (a) 19 (b) 1 (c) 2 (d) 11
  37. 37.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 3 (d) 1
  38. 38.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2⁴ × 3 × 5
  39. 39.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2⁵ × 3
  40. 40.How many factors does 15 have? (a) 5 (b) 3 (c) 2 (d) 4

Answer key

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

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