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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 66 · 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 21 have? (a) 3 (b) 4 (c) 2 (d) 5
  2. 2.How many factors does 56 have? (a) 6 (b) 8 (c) 9 (d) 7
  3. 3.How many prime numbers are there between 90 and 100? (a) 1 (b) 0 (c) 2 (d) 3
  4. 4.What is the prime factorisation of 35? (a) 5 × 7 (b) 5² × 7 (c) 5³ × 7 (d) 5 × 7²
  5. 5.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁴ × 3 (d) 2⁵ × 3
  6. 6.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
  7. 7.How many factors does 102 have? (a) 9 (b) 8 (c) 7 (d) 6
  8. 8.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
  9. 9.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 6 (d) 4
  10. 10.How many factors does 65 have? (a) 5 (b) 4 (c) 3 (d) 2
  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 209? (a) 2 (b) 11 (c) 1 (d) 19
  13. 13.How many prime numbers are there between 10 and 40? (a) 8 (b) 10 (c) 7 (d) 9
  14. 14.How many factors does 61 have? (a) 2 (b) 4 (c) 1 (d) 3
  15. 15.How many factors does 76 have? (a) 5 (b) 4 (c) 6 (d) 7
  16. 16.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5
  17. 17.How many factors does 96 have? (a) 13 (b) 10 (c) 12 (d) 11
  18. 18.What is the smallest prime factor of 95? (a) 5 (b) 2 (c) 19 (d) 1
  19. 19.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2 × 3³ (d) 2² × 3²
  20. 20.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2⁴ × 7 (d) 2³ × 7
  21. 21.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 5 (d) 6
  22. 22.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 7 (d) 9
  23. 23.How many prime numbers are there between 40 and 70? (a) 9 (b) 8 (c) 7 (d) 6
  24. 24.What is the smallest prime factor of 247? (a) 13 (b) 1 (c) 2 (d) 19
  25. 25.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
  26. 26.How many factors does 15 have? (a) 2 (b) 5 (c) 4 (d) 3
  27. 27.What is the smallest prime factor of 55? (a) 1 (b) 11 (c) 2 (d) 5
  28. 28.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 5 (d) 2
  29. 29.How many factors does 94 have? (a) 4 (b) 5 (c) 3 (d) 2
  30. 30.What is the smallest prime factor of 35? (a) 2 (b) 7 (c) 1 (d) 5
  31. 31.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 13 (d) 7
  32. 32.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 3 (d) 5
  33. 33.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
  34. 34.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  35. 35.What is the smallest prime factor of 169? (a) 2 (b) 1 (c) 3 (d) 13
  36. 36.How many factors does 38 have? (a) 4 (b) 2 (c) 5 (d) 3
  37. 37.What is the smallest prime factor of 21? (a) 2 (b) 1 (c) 7 (d) 3
  38. 38.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 4 (d) 5
  39. 39.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2⁴ × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  40. 40.How many prime numbers are there between 80 and 100? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

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

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