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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 96 · 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 99 have? (a) 6 (b) 7 (c) 4 (d) 5
  2. 2.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3 (d) 2 × 3²
  3. 3.How many factors does 102 have? (a) 6 (b) 8 (c) 9 (d) 7
  4. 4.How many prime numbers are there between 70 and 100? (a) 6 (b) 8 (c) 5 (d) 7
  5. 5.What is the smallest prime factor of 319? (a) 2 (b) 1 (c) 29 (d) 11
  6. 6.How many factors does 53 have? (a) 3 (b) 2 (c) 4 (d) 1
  7. 7.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2³ × 5 × 7
  8. 8.What is the smallest prime factor of 69? (a) 1 (b) 2 (c) 3 (d) 23
  9. 9.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2 × 5 × 7⁴
  10. 10.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2² × 3² (d) 2 × 3³
  11. 11.How many factors does 81 have? (a) 3 (b) 6 (c) 5 (d) 4
  12. 12.What is the prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3³
  13. 13.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
  14. 14.How many prime numbers are there between 30 and 40? (a) 1 (b) 3 (c) 4 (d) 2
  15. 15.How many prime numbers are there between 80 and 100? (a) 2 (b) 3 (c) 4 (d) 5
  16. 16.How many factors does 35 have? (a) 2 (b) 4 (c) 3 (d) 5
  17. 17.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3 × 5² (d) 3³ × 5
  18. 18.What is the smallest prime factor of 145? (a) 1 (b) 5 (c) 29 (d) 2
  19. 19.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 4 (d) 2
  20. 20.What is the smallest prime factor of 93? (a) 1 (b) 31 (c) 3 (d) 2
  21. 21.What is the smallest prime factor of 119? (a) 1 (b) 2 (c) 7 (d) 17
  22. 22.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5 × 7
  23. 23.How many factors does 98 have? (a) 7 (b) 5 (c) 4 (d) 6
  24. 24.How many factors does 118 have? (a) 5 (b) 4 (c) 2 (d) 3
  25. 25.How many factors does 27 have? (a) 5 (b) 3 (c) 4 (d) 2
  26. 26.How many factors does 31 have? (a) 2 (b) 4 (c) 3 (d) 1
  27. 27.How many factors does 32 have? (a) 4 (b) 7 (c) 6 (d) 5
  28. 28.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 9 (d) 6
  29. 29.How many factors does 61 have? (a) 1 (b) 3 (c) 2 (d) 4
  30. 30.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2⁵ × 3 (d) 2 × 3⁴
  31. 31.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2 × 5³ (c) 2³ × 5 (d) 2² × 5
  32. 32.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
  33. 33.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
  34. 34.How many prime numbers are there between 30 and 50? (a) 6 (b) 5 (c) 4 (d) 7
  35. 35.How many factors does 89 have? (a) 4 (b) 2 (c) 3 (d) 1
  36. 36.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2 × 3 × 7³ (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
  37. 37.What is the smallest prime factor of 217? (a) 7 (b) 1 (c) 2 (d) 31
  38. 38.How many prime numbers are there between 40 and 60? (a) 5 (b) 6 (c) 4 (d) 7
  39. 39.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
  40. 40.How many factors does 119 have? (a) 3 (b) 2 (c) 5 (d) 4

Answer key

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

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