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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 213 · 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 14 have? (a) 3 (b) 2 (c) 5 (d) 4
  2. 2.How many factors does 31 have? (a) 2 (b) 3 (c) 1 (d) 4
  3. 3.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 1 (d) 2
  4. 4.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 2 (d) 7
  5. 5.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2⁴ × 3² (d) 2² × 3²
  6. 6.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 2 (d) 13
  7. 7.What is the smallest prime factor of 187? (a) 17 (b) 11 (c) 1 (d) 2
  8. 8.What is the prime factorisation of 28? (a) 2 × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2² × 7
  9. 9.How many factors does 114 have? (a) 8 (b) 9 (c) 6 (d) 7
  10. 10.How many factors does 38 have? (a) 2 (b) 5 (c) 3 (d) 4
  11. 11.How many factors does 107 have? (a) 2 (b) 4 (c) 3 (d) 1
  12. 12.How many factors does 100 have? (a) 8 (b) 9 (c) 10 (d) 7
  13. 13.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 7 (d) 3
  14. 14.What is the smallest prime factor of 217? (a) 1 (b) 7 (c) 31 (d) 2
  15. 15.How many factors does 36 have? (a) 7 (b) 10 (c) 9 (d) 8
  16. 16.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7
  17. 17.How many factors does 61 have? (a) 1 (b) 3 (c) 4 (d) 2
  18. 18.How many factors does 112 have? (a) 11 (b) 10 (c) 8 (d) 9
  19. 19.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  20. 20.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 1 (d) 11
  21. 21.How many factors does 104 have? (a) 6 (b) 8 (c) 7 (d) 9
  22. 22.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  23. 23.How many factors does 118 have? (a) 4 (b) 2 (c) 5 (d) 3
  24. 24.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2 × 5³ (c) 2³ × 5 (d) 2² × 5
  25. 25.How many factors does 53 have? (a) 4 (b) 3 (c) 2 (d) 1
  26. 26.How many factors does 23 have? (a) 4 (b) 1 (c) 3 (d) 2
  27. 27.How many factors does 60 have? (a) 11 (b) 12 (c) 13 (d) 10
  28. 28.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 5 (d) 4
  29. 29.What is the smallest prime factor of 87? (a) 29 (b) 2 (c) 3 (d) 1
  30. 30.How many factors does 95 have? (a) 4 (b) 5 (c) 3 (d) 2
  31. 31.How many factors does 67 have? (a) 3 (b) 1 (c) 2 (d) 4
  32. 32.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2 × 3⁴ (c) 2⁴ × 3 (d) 2³ × 3
  33. 33.How many prime numbers are there between 20 and 50? (a) 7 (b) 8 (c) 6 (d) 9
  34. 34.How many prime numbers are there between 80 and 100? (a) 2 (b) 4 (c) 5 (d) 3
  35. 35.What is the smallest prime factor of 221? (a) 1 (b) 17 (c) 2 (d) 13
  36. 36.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 2 (d) 5
  37. 37.What is the smallest prime factor of 51? (a) 17 (b) 3 (c) 2 (d) 1
  38. 38.How many factors does 65 have? (a) 5 (b) 4 (c) 2 (d) 3
  39. 39.What is the smallest prime factor of 169? (a) 3 (b) 2 (c) 1 (d) 13
  40. 40.What is the smallest prime factor of 377? (a) 13 (b) 1 (c) 2 (d) 29

Answer key

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

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