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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 31 · 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 377? (a) 29 (b) 1 (c) 13 (d) 2
  2. 2.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
  3. 3.What is the smallest prime factor of 55? (a) 1 (b) 5 (c) 2 (d) 11
  4. 4.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁵ × 3 (d) 2⁴ × 3
  5. 5.How many factors does 23 have? (a) 4 (b) 3 (c) 2 (d) 1
  6. 6.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 1 (d) 5
  7. 7.How many prime numbers are there between 50 and 60? (a) 2 (b) 3 (c) 1 (d) 4
  8. 8.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 3 (d) 1
  9. 9.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3³ (d) 2⁴ × 3
  10. 10.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 4 (d) 6
  11. 11.What is the smallest prime factor of 209? (a) 2 (b) 1 (c) 11 (d) 19
  12. 12.How many factors does 120 have? (a) 16 (b) 14 (c) 15 (d) 17
  13. 13.What is the smallest prime factor of 145? (a) 2 (b) 1 (c) 5 (d) 29
  14. 14.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 2 (d) 4
  15. 15.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁵ × 3² (c) 2³ × 3² (d) 2⁴ × 3²
  16. 16.How many factors does 102 have? (a) 8 (b) 6 (c) 7 (d) 9
  17. 17.What is the prime factorisation of 21? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
  18. 18.How many factors does 62 have? (a) 2 (b) 5 (c) 4 (d) 3
  19. 19.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 4 (d) 1
  20. 20.How many factors does 37 have? (a) 2 (b) 4 (c) 1 (d) 3
  21. 21.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 1 (d) 2
  22. 22.How many factors does 33 have? (a) 4 (b) 2 (c) 3 (d) 5
  23. 23.How many factors does 14 have? (a) 3 (b) 5 (c) 2 (d) 4
  24. 24.How many factors does 117 have? (a) 4 (b) 5 (c) 6 (d) 7
  25. 25.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 5 (d) 2
  26. 26.How many factors does 106 have? (a) 2 (b) 5 (c) 4 (d) 3
  27. 27.How many factors does 20 have? (a) 4 (b) 5 (c) 7 (d) 6
  28. 28.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 5 (d) 2
  29. 29.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  30. 30.How many factors does 12 have? (a) 6 (b) 5 (c) 4 (d) 7
  31. 31.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 4 (d) 6
  32. 32.What is the prime factorisation of 12? (a) 2 × 3² (b) 2 × 3 (c) 2³ × 3 (d) 2² × 3
  33. 33.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 29 (d) 11
  34. 34.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 1 (d) 2
  35. 35.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5² × 7 (d) 5³ × 7
  36. 36.How many factors does 61 have? (a) 3 (b) 1 (c) 4 (d) 2
  37. 37.How many factors does 24 have? (a) 6 (b) 8 (c) 9 (d) 7
  38. 38.How many prime numbers are there between 50 and 70? (a) 6 (b) 5 (c) 3 (d) 4
  39. 39.How many factors does 68 have? (a) 5 (b) 7 (c) 4 (d) 6
  40. 40.How many factors does 110 have? (a) 6 (b) 7 (c) 8 (d) 9

Answer key

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

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