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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 106 · 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 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
  2. 2.How many factors does 108 have? (a) 12 (b) 11 (c) 13 (d) 10
  3. 3.How many factors does 94 have? (a) 2 (b) 5 (c) 4 (d) 3
  4. 4.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  5. 5.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2 × 5 × 7³ (c) 2⁴ × 5 × 7 (d) 2³ × 5 × 7
  6. 6.What is the prime factorisation of 63? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
  7. 7.How many factors does 72 have? (a) 10 (b) 13 (c) 12 (d) 11
  8. 8.How many factors does 83 have? (a) 3 (b) 1 (c) 2 (d) 4
  9. 9.How many factors does 19 have? (a) 4 (b) 2 (c) 3 (d) 1
  10. 10.How many factors does 58 have? (a) 5 (b) 3 (c) 2 (d) 4
  11. 11.What is the smallest prime factor of 57? (a) 19 (b) 2 (c) 1 (d) 3
  12. 12.How many factors does 95 have? (a) 4 (b) 3 (c) 5 (d) 2
  13. 13.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 2 (d) 1
  14. 14.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5²
  15. 15.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
  16. 16.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
  17. 17.How many factors does 55 have? (a) 4 (b) 2 (c) 3 (d) 5
  18. 18.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 3 (d) 5
  19. 19.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
  20. 20.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2 × 3 × 5³ (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
  21. 21.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  22. 22.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 4 (d) 2
  23. 23.How many factors does 71 have? (a) 3 (b) 1 (c) 2 (d) 4
  24. 24.How many factors does 62 have? (a) 5 (b) 4 (c) 2 (d) 3
  25. 25.How many factors does 76 have? (a) 7 (b) 4 (c) 6 (d) 5
  26. 26.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2⁴ × 5 (c) 2 × 5⁴ (d) 2³ × 5
  27. 27.How many prime numbers are there between 30 and 40? (a) 2 (b) 3 (c) 4 (d) 1
  28. 28.How many factors does 13 have? (a) 4 (b) 2 (c) 1 (d) 3
  29. 29.How many prime numbers are there between 70 and 80? (a) 3 (b) 4 (c) 2 (d) 5
  30. 30.What is the smallest prime factor of 145? (a) 5 (b) 1 (c) 2 (d) 29
  31. 31.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 11 (d) 13
  32. 32.How many prime numbers are there between 60 and 80? (a) 4 (b) 7 (c) 6 (d) 5
  33. 33.How many prime numbers are there between 10 and 40? (a) 8 (b) 10 (c) 7 (d) 9
  34. 34.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 6 (d) 9
  35. 35.What is the prime factorisation of 72? (a) 2² × 3² (b) 2² × 3³ (c) 2⁴ × 3² (d) 2³ × 3²
  36. 36.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 2 (d) 5
  37. 37.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3² × 7 (d) 3 × 7
  38. 38.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2 × 3² × 7³ (c) 2⁴ × 3² × 7 (d) 2³ × 3² × 7
  39. 39.How many prime numbers are there between 70 and 100? (a) 7 (b) 8 (c) 5 (d) 6
  40. 40.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2 × 5 × 7

Answer key

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

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