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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 103 · 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 prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 5 (d) 3
  2. 2.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2² × 7
  3. 3.How many factors does 75 have? (a) 7 (b) 5 (c) 6 (d) 4
  4. 4.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2 × 7⁴ (c) 2³ × 7 (d) 2⁴ × 7
  5. 5.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  6. 6.What is the smallest prime factor of 121? (a) 2 (b) 1 (c) 11 (d) 3
  7. 7.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 4 (d) 3
  8. 8.How many factors does 85 have? (a) 4 (b) 5 (c) 2 (d) 3
  9. 9.How many prime numbers are there between 90 and 110? (a) 7 (b) 4 (c) 5 (d) 6
  10. 10.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  11. 11.What is the prime factorisation of 12? (a) 2 × 3² (b) 2³ × 3 (c) 2 × 3 (d) 2² × 3
  12. 12.What is the prime factorisation of 40? (a) 2² × 5 (b) 2⁴ × 5 (c) 2 × 5³ (d) 2³ × 5
  13. 13.What is the smallest prime factor of 143? (a) 1 (b) 2 (c) 13 (d) 11
  14. 14.What is the smallest prime factor of 91? (a) 2 (b) 7 (c) 1 (d) 13
  15. 15.How many prime numbers are there between 40 and 70? (a) 7 (b) 8 (c) 6 (d) 9
  16. 16.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  17. 17.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 1 (d) 2
  18. 18.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 3 (d) 2
  19. 19.How many factors does 72 have? (a) 10 (b) 13 (c) 11 (d) 12
  20. 20.How many factors does 110 have? (a) 7 (b) 8 (c) 6 (d) 9
  21. 21.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 3 (d) 2
  22. 22.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2² × 7
  23. 23.What is the smallest prime factor of 119? (a) 1 (b) 2 (c) 7 (d) 17
  24. 24.What is the smallest prime factor of 155? (a) 31 (b) 5 (c) 2 (d) 1
  25. 25.What is the smallest prime factor of 55? (a) 2 (b) 11 (c) 1 (d) 5
  26. 26.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  27. 27.How many factors does 31 have? (a) 1 (b) 3 (c) 4 (d) 2
  28. 28.What is the smallest prime factor of 57? (a) 2 (b) 19 (c) 1 (d) 3
  29. 29.How many factors does 97 have? (a) 4 (b) 2 (c) 1 (d) 3
  30. 30.What is the prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7
  31. 31.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 4 (d) 1
  32. 32.How many factors does 36 have? (a) 8 (b) 7 (c) 10 (d) 9
  33. 33.How many factors does 62 have? (a) 5 (b) 4 (c) 3 (d) 2
  34. 34.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 7 (d) 4
  35. 35.How many factors does 112 have? (a) 9 (b) 10 (c) 8 (d) 11
  36. 36.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁴ × 3 (c) 2³ × 3 (d) 2⁵ × 3
  37. 37.What is the prime factorisation of 21? (a) 3 × 7 (b) 3 × 7² (c) 3² × 7 (d) 3³ × 7
  38. 38.What is the prime factorisation of 45? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
  39. 39.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2² × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2³ × 5 × 7
  40. 40.How many factors does 77 have? (a) 3 (b) 5 (c) 2 (d) 4

Answer key

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

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