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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 93 · 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 55? (a) 1 (b) 11 (c) 2 (d) 5
  2. 2.How many factors does 100 have? (a) 10 (b) 7 (c) 8 (d) 9
  3. 3.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 6 (d) 8
  4. 4.How many factors does 46 have? (a) 4 (b) 5 (c) 3 (d) 2
  5. 5.How many factors does 67 have? (a) 3 (b) 2 (c) 1 (d) 4
  6. 6.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2² × 3² × 5
  7. 7.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
  8. 8.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  9. 9.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 3 (d) 4
  10. 10.What is the smallest prime factor of 39? (a) 13 (b) 2 (c) 1 (d) 3
  11. 11.How many factors does 34 have? (a) 2 (b) 3 (c) 4 (d) 5
  12. 12.How many prime numbers are there between 50 and 70? (a) 3 (b) 4 (c) 5 (d) 6
  13. 13.What is the smallest prime factor of 253? (a) 11 (b) 23 (c) 2 (d) 1
  14. 14.What is the smallest prime factor of 377? (a) 29 (b) 13 (c) 1 (d) 2
  15. 15.How many factors does 14 have? (a) 4 (b) 5 (c) 3 (d) 2
  16. 16.What is the smallest prime factor of 169? (a) 3 (b) 1 (c) 2 (d) 13
  17. 17.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2² × 7 (d) 2⁴ × 7
  18. 18.How many factors does 27 have? (a) 3 (b) 2 (c) 5 (d) 4
  19. 19.How many prime numbers are there between 40 and 60? (a) 7 (b) 6 (c) 5 (d) 4
  20. 20.How many factors does 85 have? (a) 4 (b) 3 (c) 2 (d) 5
  21. 21.How many factors does 69 have? (a) 4 (b) 2 (c) 5 (d) 3
  22. 22.How many factors does 32 have? (a) 4 (b) 5 (c) 6 (d) 7
  23. 23.How many factors does 104 have? (a) 6 (b) 8 (c) 7 (d) 9
  24. 24.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 2 (d) 5
  25. 25.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  26. 26.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  27. 27.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁴ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
  28. 28.How many factors does 26 have? (a) 3 (b) 5 (c) 2 (d) 4
  29. 29.What is the smallest prime factor of 133? (a) 1 (b) 19 (c) 2 (d) 7
  30. 30.How many factors does 113 have? (a) 2 (b) 3 (c) 1 (d) 4
  31. 31.What is the prime factorisation of 15? (a) 3 × 5² (b) 3 × 5 (c) 3³ × 5 (d) 3² × 5
  32. 32.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 2 (d) 11
  33. 33.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2³ × 3 × 7 (d) 2⁵ × 3 × 7
  34. 34.How many factors does 109 have? (a) 1 (b) 2 (c) 3 (d) 4
  35. 35.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 1 (d) 2
  36. 36.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2² × 3 × 7
  37. 37.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 9 (d) 8
  38. 38.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7
  39. 39.How many factors does 25 have? (a) 3 (b) 1 (c) 2 (d) 4
  40. 40.How many factors does 74 have? (a) 2 (b) 5 (c) 3 (d) 4

Answer key

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

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