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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 25 · 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 smallest prime factor of 49? (a) 1 (b) 3 (c) 7 (d) 2
  2. 2.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 7 (d) 9
  3. 3.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁵ × 3 × 5 (d) 2³ × 3 × 5
  4. 4.What is the smallest prime factor of 203? (a) 29 (b) 1 (c) 2 (d) 7
  5. 5.What is the smallest prime factor of 161? (a) 7 (b) 2 (c) 1 (d) 23
  6. 6.How many factors does 54 have? (a) 7 (b) 9 (c) 6 (d) 8
  7. 7.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 1 (d) 2
  8. 8.What is the smallest prime factor of 95? (a) 1 (b) 2 (c) 5 (d) 19
  9. 9.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2⁴ × 3² × 7
  10. 10.How many prime numbers are there between 50 and 80? (a) 7 (b) 6 (c) 8 (d) 9
  11. 11.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
  12. 12.How many prime numbers are there between 40 and 60? (a) 5 (b) 4 (c) 7 (d) 6
  13. 13.How many factors does 35 have? (a) 2 (b) 5 (c) 3 (d) 4
  14. 14.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 11 (d) 7
  15. 15.How many factors does 78 have? (a) 6 (b) 9 (c) 8 (d) 7
  16. 16.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2² × 5 (c) 2⁴ × 5 (d) 2³ × 5
  17. 17.How many factors does 117 have? (a) 5 (b) 4 (c) 6 (d) 7
  18. 18.How many factors does 13 have? (a) 1 (b) 2 (c) 4 (d) 3
  19. 19.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 4 (d) 2
  20. 20.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2² × 5 (c) 2 × 5² (d) 2 × 5
  21. 21.How many factors does 22 have? (a) 4 (b) 5 (c) 3 (d) 2
  22. 22.What is the prime factorisation of 15? (a) 3 × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3² × 5
  23. 23.How many factors does 80 have? (a) 11 (b) 8 (c) 9 (d) 10
  24. 24.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 7 (d) 6
  25. 25.How many factors does 52 have? (a) 4 (b) 6 (c) 7 (d) 5
  26. 26.How many factors does 94 have? (a) 5 (b) 4 (c) 2 (d) 3
  27. 27.How many factors does 118 have? (a) 3 (b) 5 (c) 4 (d) 2
  28. 28.What is the smallest prime factor of 341? (a) 11 (b) 2 (c) 31 (d) 1
  29. 29.What is the prime factorisation of 21? (a) 3 × 7² (b) 3 × 7 (c) 3² × 7 (d) 3³ × 7
  30. 30.What is the prime factorisation of 56? (a) 2² × 7 (b) 2⁴ × 7 (c) 2³ × 7 (d) 2 × 7³
  31. 31.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 1 (d) 7
  32. 32.How many factors does 40 have? (a) 9 (b) 7 (c) 8 (d) 6
  33. 33.How many prime numbers are there between 90 and 100? (a) 0 (b) 2 (c) 1 (d) 3
  34. 34.How many factors does 89 have? (a) 2 (b) 4 (c) 1 (d) 3
  35. 35.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 1 (d) 2
  36. 36.How many factors does 107 have? (a) 2 (b) 1 (c) 4 (d) 3
  37. 37.How many prime numbers are there between 10 and 30? (a) 8 (b) 6 (c) 5 (d) 7
  38. 38.How many factors does 24 have? (a) 7 (b) 8 (c) 9 (d) 6
  39. 39.How many factors does 111 have? (a) 2 (b) 5 (c) 4 (d) 3
  40. 40.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 1 (d) 3

Answer key

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

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