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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 181 · 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 80? (a) 8 (b) 6 (c) 7 (d) 9
  2. 2.How many factors does 38 have? (a) 5 (b) 4 (c) 2 (d) 3
  3. 3.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3⁴
  4. 4.How many factors does 19 have? (a) 2 (b) 3 (c) 1 (d) 4
  5. 5.How many factors does 53 have? (a) 4 (b) 1 (c) 3 (d) 2
  6. 6.What is the prime factorisation of 21? (a) 3 × 7 (b) 3² × 7 (c) 3 × 7² (d) 3³ × 7
  7. 7.How many factors does 61 have? (a) 4 (b) 3 (c) 2 (d) 1
  8. 8.How many factors does 79 have? (a) 1 (b) 4 (c) 2 (d) 3
  9. 9.What is the smallest prime factor of 95? (a) 2 (b) 19 (c) 5 (d) 1
  10. 10.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 5 (d) 4
  11. 11.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  12. 12.What is the smallest prime factor of 169? (a) 13 (b) 2 (c) 1 (d) 3
  13. 13.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 2 (d) 3
  14. 14.How many factors does 91 have? (a) 3 (b) 5 (c) 4 (d) 2
  15. 15.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 3 (d) 5
  16. 16.What is the prime factorisation of 28? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
  17. 17.How many factors does 47 have? (a) 1 (b) 3 (c) 2 (d) 4
  18. 18.What is the smallest prime factor of 221? (a) 1 (b) 13 (c) 2 (d) 17
  19. 19.How many factors does 59 have? (a) 1 (b) 3 (c) 4 (d) 2
  20. 20.What is the smallest prime factor of 341? (a) 11 (b) 31 (c) 2 (d) 1
  21. 21.How many factors does 46 have? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.How many factors does 74 have? (a) 2 (b) 4 (c) 5 (d) 3
  23. 23.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  24. 24.What is the smallest prime factor of 69? (a) 1 (b) 23 (c) 2 (d) 3
  25. 25.What is the smallest prime factor of 93? (a) 1 (b) 3 (c) 31 (d) 2
  26. 26.What is the prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  27. 27.How many factors does 103 have? (a) 3 (b) 2 (c) 1 (d) 4
  28. 28.How many factors does 78 have? (a) 8 (b) 6 (c) 7 (d) 9
  29. 29.How many factors does 110 have? (a) 8 (b) 6 (c) 7 (d) 9
  30. 30.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
  31. 31.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 7 (d) 8
  32. 32.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7³ (d) 2⁴ × 3² × 7
  33. 33.How many factors does 50 have? (a) 5 (b) 6 (c) 4 (d) 7
  34. 34.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 6 (d) 4
  35. 35.How many factors does 25 have? (a) 3 (b) 2 (c) 4 (d) 1
  36. 36.What is the smallest prime factor of 377? (a) 2 (b) 1 (c) 29 (d) 13
  37. 37.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2 × 3²
  38. 38.How many factors does 102 have? (a) 6 (b) 7 (c) 9 (d) 8
  39. 39.How many factors does 23 have? (a) 3 (b) 4 (c) 1 (d) 2
  40. 40.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5

Answer key

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

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