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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 21 · 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 prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  2. 2.How many factors does 16 have? (a) 6 (b) 4 (c) 3 (d) 5
  3. 3.How many factors does 26 have? (a) 2 (b) 5 (c) 3 (d) 4
  4. 4.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2⁵ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2³ × 5 × 7
  5. 5.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
  6. 6.How many prime numbers are there between 80 and 110? (a) 7 (b) 6 (c) 9 (d) 8
  7. 7.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 1 (d) 11
  8. 8.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 7 (d) 9
  9. 9.How many factors does 80 have? (a) 9 (b) 11 (c) 8 (d) 10
  10. 10.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
  11. 11.How many factors does 79 have? (a) 1 (b) 3 (c) 4 (d) 2
  12. 12.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 5 (d) 6
  13. 13.How many factors does 85 have? (a) 5 (b) 2 (c) 4 (d) 3
  14. 14.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 2 (d) 4
  15. 15.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2 × 3² × 7 (d) 2² × 3² × 7
  16. 16.How many factors does 62 have? (a) 5 (b) 4 (c) 3 (d) 2
  17. 17.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 7 (d) 6
  18. 18.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 7 (d) 1
  19. 19.How many factors does 52 have? (a) 4 (b) 6 (c) 7 (d) 5
  20. 20.How many factors does 103 have? (a) 4 (b) 1 (c) 3 (d) 2
  21. 21.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 4 (d) 6
  22. 22.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 1 (d) 2
  23. 23.How many factors does 116 have? (a) 7 (b) 6 (c) 4 (d) 5
  24. 24.How many factors does 74 have? (a) 3 (b) 2 (c) 4 (d) 5
  25. 25.What is the smallest prime factor of 33? (a) 1 (b) 3 (c) 2 (d) 11
  26. 26.What is the smallest prime factor of 209? (a) 2 (b) 11 (c) 1 (d) 19
  27. 27.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 2 (d) 1
  28. 28.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 11 (d) 2
  29. 29.How many factors does 18 have? (a) 5 (b) 6 (c) 7 (d) 4
  30. 30.How many factors does 40 have? (a) 7 (b) 6 (c) 9 (d) 8
  31. 31.How many factors does 97 have? (a) 1 (b) 2 (c) 3 (d) 4
  32. 32.How many factors does 119 have? (a) 3 (b) 2 (c) 5 (d) 4
  33. 33.What is the smallest prime factor of 35? (a) 5 (b) 1 (c) 7 (d) 2
  34. 34.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 1 (d) 2
  35. 35.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2⁴ × 3² × 5 (c) 2³ × 3² × 5 (d) 2² × 3² × 5
  36. 36.How many factors does 57 have? (a) 4 (b) 2 (c) 3 (d) 5
  37. 37.What is the smallest prime factor of 65? (a) 5 (b) 13 (c) 2 (d) 1
  38. 38.What is the smallest prime factor of 93? (a) 2 (b) 3 (c) 1 (d) 31
  39. 39.What is the smallest prime factor of 95? (a) 19 (b) 5 (c) 2 (d) 1
  40. 40.How many factors does 47 have? (a) 3 (b) 1 (c) 2 (d) 4

Answer key

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

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