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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 37 · 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 102 have? (a) 7 (b) 8 (c) 9 (d) 6
  2. 2.How many factors does 24 have? (a) 6 (b) 9 (c) 8 (d) 7
  3. 3.How many factors does 40 have? (a) 6 (b) 7 (c) 9 (d) 8
  4. 4.How many factors does 81 have? (a) 6 (b) 5 (c) 3 (d) 4
  5. 5.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5
  6. 6.What is the smallest prime factor of 49? (a) 3 (b) 2 (c) 1 (d) 7
  7. 7.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2² × 3 (c) 2⁴ × 3 (d) 2³ × 3
  8. 8.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
  9. 9.What is the smallest prime factor of 69? (a) 3 (b) 1 (c) 2 (d) 23
  10. 10.What is the smallest prime factor of 77? (a) 1 (b) 7 (c) 11 (d) 2
  11. 11.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
  12. 12.How many factors does 59 have? (a) 2 (b) 4 (c) 3 (d) 1
  13. 13.How many prime numbers are there between 10 and 20? (a) 5 (b) 4 (c) 6 (d) 3
  14. 14.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 6 (d) 7
  15. 15.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 9 (d) 8
  16. 16.What is the smallest prime factor of 93? (a) 2 (b) 1 (c) 31 (d) 3
  17. 17.What is the smallest prime factor of 169? (a) 3 (b) 1 (c) 13 (d) 2
  18. 18.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 6 (d) 5
  19. 19.What is the smallest prime factor of 85? (a) 1 (b) 2 (c) 5 (d) 17
  20. 20.How many factors does 34 have? (a) 2 (b) 3 (c) 5 (d) 4
  21. 21.How many prime numbers are there between 40 and 70? (a) 6 (b) 9 (c) 8 (d) 7
  22. 22.What is the smallest prime factor of 341? (a) 11 (b) 2 (c) 1 (d) 31
  23. 23.What is the prime factorisation of 63? (a) 3 × 7² (b) 3 × 7 (c) 3² × 7 (d) 3³ × 7
  24. 24.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  25. 25.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  26. 26.How many factors does 73 have? (a) 2 (b) 4 (c) 3 (d) 1
  27. 27.What is the prime factorisation of 28? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
  28. 28.How many factors does 100 have? (a) 7 (b) 8 (c) 9 (d) 10
  29. 29.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 1 (d) 2
  30. 30.How many factors does 71 have? (a) 2 (b) 3 (c) 4 (d) 1
  31. 31.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  32. 32.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
  33. 33.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 23 (d) 7
  34. 34.How many prime numbers are there between 90 and 110? (a) 5 (b) 7 (c) 6 (d) 4
  35. 35.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁴ × 5 (c) 2⁵ × 5 (d) 2³ × 5
  36. 36.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2² × 5
  37. 37.How many prime numbers are there between 80 and 100? (a) 3 (b) 2 (c) 5 (d) 4
  38. 38.How many factors does 80 have? (a) 10 (b) 8 (c) 11 (d) 9
  39. 39.How many factors does 36 have? (a) 9 (b) 10 (c) 8 (d) 7
  40. 40.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2² × 7 (d) 2⁴ × 7

Answer key

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

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