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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 215 · 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 71 have? (a) 2 (b) 1 (c) 4 (d) 3
  2. 2.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2⁴ × 7 (d) 2 × 7³
  3. 3.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
  4. 4.How many factors does 118 have? (a) 4 (b) 2 (c) 3 (d) 5
  5. 5.How many factors does 21 have? (a) 5 (b) 3 (c) 4 (d) 2
  6. 6.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 1 (d) 7
  7. 7.How many prime numbers are there between 40 and 60? (a) 7 (b) 6 (c) 5 (d) 4
  8. 8.How many factors does 35 have? (a) 5 (b) 4 (c) 2 (d) 3
  9. 9.How many factors does 78 have? (a) 7 (b) 9 (c) 6 (d) 8
  10. 10.What is the smallest prime factor of 115? (a) 1 (b) 2 (c) 23 (d) 5
  11. 11.How many factors does 103 have? (a) 3 (b) 1 (c) 4 (d) 2
  12. 12.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 3 (d) 1
  13. 13.How many factors does 39 have? (a) 2 (b) 3 (c) 4 (d) 5
  14. 14.What is the smallest prime factor of 145? (a) 5 (b) 2 (c) 1 (d) 29
  15. 15.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3 (c) 2² × 3² (d) 2 × 3²
  16. 16.What is the smallest prime factor of 87? (a) 2 (b) 29 (c) 3 (d) 1
  17. 17.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
  18. 18.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2 × 3² × 7³ (c) 2² × 3² × 7 (d) 2⁴ × 3² × 7
  19. 19.How many prime numbers are there between 40 and 70? (a) 6 (b) 7 (c) 8 (d) 9
  20. 20.How many factors does 83 have? (a) 1 (b) 3 (c) 2 (d) 4
  21. 21.How many factors does 90 have? (a) 13 (b) 11 (c) 12 (d) 10
  22. 22.How many prime numbers are there between 90 and 100? (a) 1 (b) 0 (c) 2 (d) 3
  23. 23.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 8 (d) 7
  24. 24.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 5 (d) 7
  25. 25.How many factors does 51 have? (a) 2 (b) 4 (c) 3 (d) 5
  26. 26.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7 (d) 3 × 7²
  27. 27.How many factors does 99 have? (a) 7 (b) 4 (c) 5 (d) 6
  28. 28.How many factors does 48 have? (a) 8 (b) 9 (c) 11 (d) 10
  29. 29.How many factors does 27 have? (a) 2 (b) 4 (c) 3 (d) 5
  30. 30.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2 × 5³ (c) 2² × 5 (d) 2⁴ × 5
  31. 31.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 2 (d) 1
  32. 32.What is the prime factorisation of 28? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2 × 7
  33. 33.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  34. 34.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 2 (d) 11
  35. 35.How many factors does 102 have? (a) 8 (b) 6 (c) 7 (d) 9
  36. 36.What is the smallest prime factor of 85? (a) 2 (b) 17 (c) 5 (d) 1
  37. 37.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  38. 38.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3³ × 5 × 7
  39. 39.What is the smallest prime factor of 49? (a) 7 (b) 1 (c) 3 (d) 2
  40. 40.How many factors does 70 have? (a) 7 (b) 8 (c) 9 (d) 6

Answer key

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

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