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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 122 · 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 factors does 58 have? (a) 2 (b) 4 (c) 5 (d) 3
  2. 2.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2 × 5⁴ (c) 2⁵ × 5 (d) 2⁴ × 5
  3. 3.How many factors does 15 have? (a) 3 (b) 2 (c) 5 (d) 4
  4. 4.How many factors does 103 have? (a) 3 (b) 2 (c) 4 (d) 1
  5. 5.What is the smallest prime factor of 169? (a) 13 (b) 3 (c) 1 (d) 2
  6. 6.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2² × 3⁴ (d) 2⁴ × 3²
  7. 7.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
  8. 8.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
  9. 9.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  10. 10.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  11. 11.How many prime numbers are there between 10 and 30? (a) 5 (b) 6 (c) 7 (d) 8
  12. 12.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 2 (d) 3
  13. 13.How many factors does 69 have? (a) 5 (b) 3 (c) 4 (d) 2
  14. 14.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  15. 15.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 1 (d) 5
  16. 16.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
  17. 17.What is the smallest prime factor of 209? (a) 19 (b) 1 (c) 11 (d) 2
  18. 18.What is the smallest prime factor of 377? (a) 13 (b) 29 (c) 1 (d) 2
  19. 19.How many factors does 98 have? (a) 6 (b) 4 (c) 7 (d) 5
  20. 20.How many prime numbers are there between 30 and 40? (a) 4 (b) 2 (c) 3 (d) 1
  21. 21.How many prime numbers are there between 70 and 90? (a) 4 (b) 7 (c) 6 (d) 5
  22. 22.How many factors does 20 have? (a) 4 (b) 5 (c) 7 (d) 6
  23. 23.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
  24. 24.How many factors does 27 have? (a) 4 (b) 3 (c) 5 (d) 2
  25. 25.How many factors does 94 have? (a) 2 (b) 4 (c) 5 (d) 3
  26. 26.How many factors does 46 have? (a) 2 (b) 4 (c) 3 (d) 5
  27. 27.How many factors does 87 have? (a) 2 (b) 4 (c) 5 (d) 3
  28. 28.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 6 (d) 7
  29. 29.How many factors does 24 have? (a) 6 (b) 8 (c) 9 (d) 7
  30. 30.How many factors does 29 have? (a) 3 (b) 1 (c) 2 (d) 4
  31. 31.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 1 (d) 2
  32. 32.How many factors does 66 have? (a) 7 (b) 9 (c) 8 (d) 6
  33. 33.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 5 (d) 4
  34. 34.How many factors does 36 have? (a) 7 (b) 9 (c) 8 (d) 10
  35. 35.What is the smallest prime factor of 319? (a) 2 (b) 29 (c) 11 (d) 1
  36. 36.How many factors does 117 have? (a) 4 (b) 7 (c) 6 (d) 5
  37. 37.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2⁴ × 5 × 7
  38. 38.How many prime numbers are there between 50 and 60? (a) 1 (b) 2 (c) 3 (d) 4
  39. 39.How many factors does 12 have? (a) 4 (b) 7 (c) 5 (d) 6
  40. 40.How many factors does 113 have? (a) 4 (b) 3 (c) 2 (d) 1

Answer key

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

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