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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 39 · 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 prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4
  2. 2.How many prime numbers are there between 20 and 50? (a) 6 (b) 9 (c) 8 (d) 7
  3. 3.How many factors does 19 have? (a) 1 (b) 3 (c) 2 (d) 4
  4. 4.What is the smallest prime factor of 169? (a) 3 (b) 2 (c) 13 (d) 1
  5. 5.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 10 (d) 9
  6. 6.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2³ × 5 × 7
  7. 7.What is the smallest prime factor of 247? (a) 19 (b) 1 (c) 2 (d) 13
  8. 8.What is the smallest prime factor of 35? (a) 7 (b) 2 (c) 5 (d) 1
  9. 9.What is the smallest prime factor of 55? (a) 11 (b) 2 (c) 5 (d) 1
  10. 10.How many factors does 85 have? (a) 2 (b) 4 (c) 5 (d) 3
  11. 11.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
  12. 12.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 11 (d) 2
  13. 13.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  14. 14.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 1 (d) 11
  15. 15.How many prime numbers are there between 50 and 70? (a) 5 (b) 6 (c) 4 (d) 3
  16. 16.What is the smallest prime factor of 203? (a) 1 (b) 2 (c) 29 (d) 7
  17. 17.What is the prime factorisation of 28? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  18. 18.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 13 (d) 1
  19. 19.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁵ × 3 × 5 (d) 2³ × 3 × 5
  20. 20.How many factors does 27 have? (a) 4 (b) 2 (c) 3 (d) 5
  21. 21.What is the smallest prime factor of 87? (a) 3 (b) 29 (c) 1 (d) 2
  22. 22.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3²
  23. 23.How many factors does 32 have? (a) 6 (b) 5 (c) 7 (d) 4
  24. 24.How many factors does 62 have? (a) 2 (b) 5 (c) 4 (d) 3
  25. 25.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5 × 7² (c) 5 × 7 (d) 5² × 7
  26. 26.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2³ × 7
  27. 27.How many factors does 34 have? (a) 3 (b) 4 (c) 5 (d) 2
  28. 28.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 3 (d) 4
  29. 29.How many factors does 37 have? (a) 1 (b) 3 (c) 2 (d) 4
  30. 30.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 13 (d) 5
  31. 31.How many prime numbers are there between 60 and 80? (a) 4 (b) 7 (c) 6 (d) 5
  32. 32.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 1 (d) 4
  33. 33.How many factors does 94 have? (a) 4 (b) 3 (c) 2 (d) 5
  34. 34.How many factors does 52 have? (a) 5 (b) 4 (c) 6 (d) 7
  35. 35.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
  36. 36.How many factors does 23 have? (a) 4 (b) 2 (c) 1 (d) 3
  37. 37.What is the smallest prime factor of 57? (a) 3 (b) 2 (c) 19 (d) 1
  38. 38.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 11 (d) 2
  39. 39.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 8 (d) 5
  40. 40.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6

Answer key

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

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