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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 174 · 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 50 and 60? (a) 3 (b) 2 (c) 4 (d) 1
  2. 2.How many factors does 70 have? (a) 9 (b) 8 (c) 6 (d) 7
  3. 3.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 7 (d) 13
  4. 4.How many factors does 57 have? (a) 4 (b) 2 (c) 5 (d) 3
  5. 5.How many factors does 66 have? (a) 7 (b) 8 (c) 9 (d) 6
  6. 6.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁴ × 3² (c) 2³ × 3² (d) 2⁵ × 3²
  7. 7.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 6 (d) 5
  8. 8.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
  9. 9.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3² (c) 2⁴ × 3² (d) 2² × 3³
  10. 10.How many prime numbers are there between 40 and 60? (a) 6 (b) 4 (c) 7 (d) 5
  11. 11.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 1 (d) 2
  12. 12.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 2 (d) 1
  13. 13.How many factors does 67 have? (a) 3 (b) 2 (c) 1 (d) 4
  14. 14.How many factors does 118 have? (a) 3 (b) 5 (c) 2 (d) 4
  15. 15.What is the smallest prime factor of 33? (a) 11 (b) 2 (c) 1 (d) 3
  16. 16.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 2 (d) 5
  17. 17.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
  18. 18.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  19. 19.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 2 (d) 5
  20. 20.How many factors does 108 have? (a) 13 (b) 12 (c) 10 (d) 11
  21. 21.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5³ (d) 2⁴ × 5
  22. 22.How many prime numbers are there between 30 and 40? (a) 1 (b) 2 (c) 3 (d) 4
  23. 23.How many factors does 60 have? (a) 13 (b) 11 (c) 10 (d) 12
  24. 24.What is the smallest prime factor of 49? (a) 1 (b) 3 (c) 7 (d) 2
  25. 25.How many factors does 89 have? (a) 3 (b) 2 (c) 4 (d) 1
  26. 26.What is the prime factorisation of 12? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3² (d) 2 × 3
  27. 27.How many factors does 35 have? (a) 4 (b) 3 (c) 2 (d) 5
  28. 28.How many prime numbers are there between 90 and 120? (a) 6 (b) 5 (c) 7 (d) 8
  29. 29.How many factors does 68 have? (a) 4 (b) 5 (c) 7 (d) 6
  30. 30.What is the smallest prime factor of 341? (a) 2 (b) 11 (c) 31 (d) 1
  31. 31.How many factors does 63 have? (a) 5 (b) 6 (c) 4 (d) 7
  32. 32.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 11 (d) 2
  33. 33.How many factors does 30 have? (a) 6 (b) 7 (c) 8 (d) 9
  34. 34.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 7 (d) 5
  35. 35.How many prime numbers are there between 90 and 100? (a) 3 (b) 2 (c) 0 (d) 1
  36. 36.How many factors does 74 have? (a) 5 (b) 3 (c) 2 (d) 4
  37. 37.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 11 (d) 7
  38. 38.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 29 (d) 2
  39. 39.How many factors does 46 have? (a) 3 (b) 2 (c) 4 (d) 5
  40. 40.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2² × 5 × 7

Answer key

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

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