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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 147 · 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 115? (a) 23 (b) 2 (c) 5 (d) 1
  2. 2.How many factors does 49 have? (a) 1 (b) 2 (c) 4 (d) 3
  3. 3.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 9 (d) 7
  4. 4.What is the smallest prime factor of 133? (a) 1 (b) 2 (c) 19 (d) 7
  5. 5.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
  6. 6.How many factors does 78 have? (a) 6 (b) 9 (c) 8 (d) 7
  7. 7.How many factors does 25 have? (a) 4 (b) 1 (c) 3 (d) 2
  8. 8.How many factors does 85 have? (a) 2 (b) 4 (c) 5 (d) 3
  9. 9.How many factors does 118 have? (a) 2 (b) 4 (c) 3 (d) 5
  10. 10.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 5 (d) 8
  11. 11.How many factors does 63 have? (a) 6 (b) 4 (c) 5 (d) 7
  12. 12.How many factors does 103 have? (a) 3 (b) 1 (c) 4 (d) 2
  13. 13.How many factors does 44 have? (a) 4 (b) 6 (c) 5 (d) 7
  14. 14.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
  15. 15.What is the smallest prime factor of 217? (a) 31 (b) 7 (c) 2 (d) 1
  16. 16.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  17. 17.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5³ (d) 2² × 3 × 5
  18. 18.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3³ (c) 2³ × 3² (d) 2² × 3²
  19. 19.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7³
  20. 20.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5³
  21. 21.How many factors does 105 have? (a) 9 (b) 8 (c) 6 (d) 7
  22. 22.What is the smallest prime factor of 209? (a) 1 (b) 19 (c) 11 (d) 2
  23. 23.How many prime numbers are there between 30 and 50? (a) 6 (b) 7 (c) 5 (d) 4
  24. 24.How many prime numbers are there between 20 and 40? (a) 4 (b) 5 (c) 6 (d) 3
  25. 25.How many prime numbers are there between 50 and 70? (a) 5 (b) 4 (c) 3 (d) 6
  26. 26.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2³ × 3 × 5 (d) 2⁴ × 3 × 5
  27. 27.What is the smallest prime factor of 39? (a) 3 (b) 1 (c) 2 (d) 13
  28. 28.What is the smallest prime factor of 57? (a) 1 (b) 19 (c) 2 (d) 3
  29. 29.How many factors does 42 have? (a) 8 (b) 6 (c) 7 (d) 9
  30. 30.How many prime numbers are there between 80 and 110? (a) 9 (b) 7 (c) 8 (d) 6
  31. 31.What is the smallest prime factor of 49? (a) 2 (b) 1 (c) 7 (d) 3
  32. 32.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7³
  33. 33.What is the prime factorisation of 63? (a) 3 × 7 (b) 3 × 7² (c) 3² × 7 (d) 3³ × 7
  34. 34.How many factors does 22 have? (a) 3 (b) 2 (c) 4 (d) 5
  35. 35.How many factors does 47 have? (a) 4 (b) 3 (c) 1 (d) 2
  36. 36.How many factors does 100 have? (a) 8 (b) 7 (c) 10 (d) 9
  37. 37.How many prime numbers are there between 10 and 40? (a) 7 (b) 10 (c) 8 (d) 9
  38. 38.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
  39. 39.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
  40. 40.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5

Answer key

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

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