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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 146 · 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 smallest prime factor of 145? (a) 1 (b) 5 (c) 29 (d) 2
  2. 2.How many prime numbers are there between 10 and 40? (a) 8 (b) 10 (c) 7 (d) 9
  3. 3.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 7 (d) 1
  4. 4.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2² × 3 × 7 (d) 2 × 3 × 7
  5. 5.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 6 (d) 4
  6. 6.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 5 (d) 2
  8. 8.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  9. 9.What is the smallest prime factor of 21? (a) 2 (b) 3 (c) 7 (d) 1
  10. 10.How many factors does 42 have? (a) 9 (b) 7 (c) 8 (d) 6
  11. 11.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 9 (d) 7
  12. 12.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  13. 13.How many factors does 17 have? (a) 2 (b) 4 (c) 3 (d) 1
  14. 14.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 2 (d) 31
  15. 15.What is the smallest prime factor of 187? (a) 11 (b) 17 (c) 1 (d) 2
  16. 16.How many factors does 18 have? (a) 6 (b) 5 (c) 7 (d) 4
  17. 17.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  18. 18.How many factors does 84 have? (a) 11 (b) 12 (c) 13 (d) 10
  19. 19.How many factors does 69 have? (a) 4 (b) 2 (c) 3 (d) 5
  20. 20.What is the smallest prime factor of 169? (a) 2 (b) 1 (c) 13 (d) 3
  21. 21.What is the smallest prime factor of 133? (a) 1 (b) 19 (c) 2 (d) 7
  22. 22.How many factors does 93 have? (a) 5 (b) 2 (c) 3 (d) 4
  23. 23.How many factors does 47 have? (a) 1 (b) 3 (c) 2 (d) 4
  24. 24.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 6 (d) 5
  25. 25.How many factors does 115 have? (a) 5 (b) 2 (c) 3 (d) 4
  26. 26.How many factors does 25 have? (a) 1 (b) 2 (c) 3 (d) 4
  27. 27.How many prime numbers are there between 20 and 40? (a) 4 (b) 5 (c) 3 (d) 6
  28. 28.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
  29. 29.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 2 (d) 4
  30. 30.What is the smallest prime factor of 143? (a) 11 (b) 1 (c) 2 (d) 13
  31. 31.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 11 (d) 1
  32. 32.How many factors does 114 have? (a) 6 (b) 7 (c) 8 (d) 9
  33. 33.What is the smallest prime factor of 39? (a) 1 (b) 2 (c) 3 (d) 13
  34. 34.How many factors does 65 have? (a) 4 (b) 2 (c) 5 (d) 3
  35. 35.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2 × 5³ (c) 2² × 5 (d) 2³ × 5
  36. 36.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7² (c) 3² × 7 (d) 3 × 7
  37. 37.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7 (c) 2² × 7 (d) 2 × 7²
  38. 38.What is the smallest prime factor of 57? (a) 3 (b) 19 (c) 1 (d) 2
  39. 39.How many prime numbers are there between 20 and 30? (a) 2 (b) 3 (c) 1 (d) 4
  40. 40.How many prime numbers are there between 90 and 110? (a) 7 (b) 5 (c) 4 (d) 6

Answer key

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

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