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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 36 · 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 40? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5³ (d) 2⁴ × 5
  2. 2.How many factors does 45 have? (a) 4 (b) 7 (c) 6 (d) 5
  3. 3.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 6 (d) 9
  4. 4.How many factors does 67 have? (a) 4 (b) 1 (c) 2 (d) 3
  5. 5.How many factors does 113 have? (a) 3 (b) 2 (c) 1 (d) 4
  6. 6.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3³
  7. 7.How many factors does 112 have? (a) 9 (b) 10 (c) 8 (d) 11
  8. 8.What is the smallest prime factor of 247? (a) 13 (b) 1 (c) 2 (d) 19
  9. 9.How many factors does 94 have? (a) 4 (b) 3 (c) 5 (d) 2
  10. 10.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 7 (d) 9
  11. 11.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
  12. 12.What is the smallest prime factor of 77? (a) 1 (b) 7 (c) 11 (d) 2
  13. 13.How many factors does 100 have? (a) 9 (b) 8 (c) 7 (d) 10
  14. 14.How many factors does 72 have? (a) 10 (b) 12 (c) 13 (d) 11
  15. 15.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
  16. 16.How many prime numbers are there between 40 and 50? (a) 2 (b) 3 (c) 4 (d) 5
  17. 17.How many factors does 115 have? (a) 4 (b) 2 (c) 3 (d) 5
  18. 18.How many factors does 116 have? (a) 4 (b) 6 (c) 5 (d) 7
  19. 19.What is the smallest prime factor of 377? (a) 29 (b) 13 (c) 2 (d) 1
  20. 20.How many factors does 81 have? (a) 4 (b) 6 (c) 3 (d) 5
  21. 21.How many factors does 83 have? (a) 2 (b) 3 (c) 4 (d) 1
  22. 22.How many factors does 41 have? (a) 1 (b) 2 (c) 3 (d) 4
  23. 23.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5 (c) 3³ × 5 (d) 3 × 5²
  24. 24.How many factors does 66 have? (a) 9 (b) 6 (c) 7 (d) 8
  25. 25.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  26. 26.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
  27. 27.How many factors does 42 have? (a) 8 (b) 7 (c) 6 (d) 9
  28. 28.How many factors does 12 have? (a) 4 (b) 5 (c) 7 (d) 6
  29. 29.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2 × 3² × 7
  30. 30.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2² × 5 (c) 2 × 5² (d) 2 × 5
  31. 31.How many factors does 57 have? (a) 3 (b) 2 (c) 4 (d) 5
  32. 32.What is the smallest prime factor of 221? (a) 13 (b) 2 (c) 17 (d) 1
  33. 33.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  34. 34.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 1 (d) 31
  35. 35.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2⁴ × 3² (c) 2³ × 3² (d) 2² × 3⁴
  36. 36.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  37. 37.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 3 (d) 0
  38. 38.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  39. 39.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 4 (d) 3
  40. 40.How many factors does 111 have? (a) 2 (b) 5 (c) 4 (d) 3

Answer key

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

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