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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 158 · 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 49? (a) 3 (b) 2 (c) 1 (d) 7
  2. 2.How many factors does 110 have? (a) 8 (b) 6 (c) 9 (d) 7
  3. 3.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 4 (d) 6
  4. 4.How many factors does 33 have? (a) 4 (b) 5 (c) 2 (d) 3
  5. 5.How many factors does 80 have? (a) 8 (b) 9 (c) 10 (d) 11
  6. 6.How many factors does 19 have? (a) 3 (b) 4 (c) 2 (d) 1
  7. 7.What is the smallest prime factor of 57? (a) 19 (b) 1 (c) 3 (d) 2
  8. 8.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  9. 9.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 1 (d) 4
  10. 10.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 1 (d) 4
  11. 11.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 4 (d) 3
  12. 12.How many prime numbers are there between 30 and 60? (a) 7 (b) 6 (c) 9 (d) 8
  13. 13.What is the prime factorisation of 63? (a) 3 × 7² (b) 3 × 7 (c) 3³ × 7 (d) 3² × 7
  14. 14.How many factors does 86 have? (a) 2 (b) 4 (c) 3 (d) 5
  15. 15.What is the smallest prime factor of 33? (a) 11 (b) 3 (c) 2 (d) 1
  16. 16.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  17. 17.How many factors does 90 have? (a) 11 (b) 12 (c) 13 (d) 10
  18. 18.How many factors does 96 have? (a) 11 (b) 12 (c) 10 (d) 13
  19. 19.How many prime numbers are there between 70 and 90? (a) 4 (b) 5 (c) 7 (d) 6
  20. 20.How many prime numbers are there between 40 and 50? (a) 5 (b) 4 (c) 3 (d) 2
  21. 21.How many factors does 38 have? (a) 4 (b) 3 (c) 2 (d) 5
  22. 22.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
  23. 23.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13
  24. 24.How many factors does 63 have? (a) 5 (b) 6 (c) 4 (d) 7
  25. 25.What is the prime factorisation of 56? (a) 2² × 7 (b) 2⁴ × 7 (c) 2 × 7³ (d) 2³ × 7
  26. 26.How many factors does 92 have? (a) 4 (b) 6 (c) 5 (d) 7
  27. 27.How many factors does 117 have? (a) 4 (b) 7 (c) 6 (d) 5
  28. 28.How many prime numbers are there between 20 and 40? (a) 4 (b) 5 (c) 3 (d) 6
  29. 29.What is the prime factorisation of 12? (a) 2 × 3² (b) 2³ × 3 (c) 2 × 3 (d) 2² × 3
  30. 30.How many factors does 108 have? (a) 11 (b) 13 (c) 10 (d) 12
  31. 31.How many prime numbers are there between 10 and 40? (a) 9 (b) 8 (c) 10 (d) 7
  32. 32.What is the smallest prime factor of 247? (a) 2 (b) 13 (c) 1 (d) 19
  33. 33.How many factors does 49 have? (a) 3 (b) 1 (c) 4 (d) 2
  34. 34.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
  35. 35.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 2 (d) 5
  36. 36.How many factors does 31 have? (a) 1 (b) 2 (c) 4 (d) 3
  37. 37.How many factors does 98 have? (a) 4 (b) 6 (c) 5 (d) 7
  38. 38.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 1 (d) 2
  39. 39.How many factors does 67 have? (a) 2 (b) 3 (c) 4 (d) 1
  40. 40.How many factors does 32 have? (a) 6 (b) 4 (c) 5 (d) 7

Answer key

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

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