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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 88 · 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 43 have? (a) 3 (b) 1 (c) 4 (d) 2
  2. 2.How many factors does 92 have? (a) 7 (b) 5 (c) 4 (d) 6
  3. 3.How many factors does 46 have? (a) 3 (b) 5 (c) 2 (d) 4
  4. 4.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 4 (d) 1
  5. 5.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5³
  6. 6.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 1 (d) 11
  7. 7.What is the smallest prime factor of 39? (a) 13 (b) 2 (c) 3 (d) 1
  8. 8.How many prime numbers are there between 90 and 120? (a) 8 (b) 5 (c) 7 (d) 6
  9. 9.How many factors does 103 have? (a) 3 (b) 1 (c) 4 (d) 2
  10. 10.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  11. 11.What is the smallest prime factor of 87? (a) 2 (b) 3 (c) 29 (d) 1
  12. 12.What is the prime factorisation of 20? (a) 2 × 5² (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5
  13. 13.How many factors does 78 have? (a) 8 (b) 7 (c) 9 (d) 6
  14. 14.What is the smallest prime factor of 377? (a) 29 (b) 13 (c) 1 (d) 2
  15. 15.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 2 (d) 1
  16. 16.How many factors does 88 have? (a) 8 (b) 6 (c) 7 (d) 9
  17. 17.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  18. 18.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 7 (d) 8
  19. 19.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 2 (d) 1
  20. 20.How many factors does 16 have? (a) 5 (b) 3 (c) 6 (d) 4
  21. 21.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2 × 7⁴ (c) 2³ × 7 (d) 2⁵ × 7
  22. 22.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
  23. 23.How many factors does 68 have? (a) 7 (b) 5 (c) 6 (d) 4
  24. 24.What is the prime factorisation of 40? (a) 2² × 5 (b) 2⁴ × 5 (c) 2 × 5³ (d) 2³ × 5
  25. 25.What is the smallest prime factor of 209? (a) 2 (b) 1 (c) 19 (d) 11
  26. 26.How many factors does 91 have? (a) 5 (b) 3 (c) 4 (d) 2
  27. 27.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
  28. 28.How many factors does 64 have? (a) 5 (b) 6 (c) 8 (d) 7
  29. 29.How many prime numbers are there between 90 and 110? (a) 4 (b) 5 (c) 6 (d) 7
  30. 30.How many prime numbers are there between 60 and 90? (a) 7 (b) 6 (c) 9 (d) 8
  31. 31.How many factors does 32 have? (a) 4 (b) 7 (c) 6 (d) 5
  32. 32.How many prime numbers are there between 60 and 70? (a) 2 (b) 1 (c) 3 (d) 4
  33. 33.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 7 (d) 5
  34. 34.How many factors does 119 have? (a) 2 (b) 4 (c) 3 (d) 5
  35. 35.How many factors does 73 have? (a) 4 (b) 2 (c) 3 (d) 1
  36. 36.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2³ × 3 (c) 2⁴ × 3 (d) 2² × 3
  37. 37.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 5 (d) 6
  38. 38.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 2 (d) 7
  39. 39.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7 (c) 2 × 7² (d) 2³ × 7
  40. 40.How many factors does 56 have? (a) 8 (b) 7 (c) 9 (d) 6

Answer key

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

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