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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 137 · 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 133? (a) 1 (b) 19 (c) 7 (d) 2
  2. 2.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
  3. 3.How many factors does 89 have? (a) 3 (b) 2 (c) 4 (d) 1
  4. 4.What is the prime factorisation of 14? (a) 2 × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7²
  5. 5.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 0 (d) 3
  6. 6.How many prime numbers are there between 80 and 100? (a) 2 (b) 4 (c) 5 (d) 3
  7. 7.How many factors does 28 have? (a) 5 (b) 6 (c) 7 (d) 4
  8. 8.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 4 (d) 6
  9. 9.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 7 (d) 2
  10. 10.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 2 (d) 7
  11. 11.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 2 (d) 3
  12. 12.How many prime numbers are there between 30 and 40? (a) 1 (b) 3 (c) 2 (d) 4
  13. 13.How many factors does 37 have? (a) 4 (b) 3 (c) 2 (d) 1
  14. 14.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 6 (d) 4
  15. 15.What is the smallest prime factor of 51? (a) 3 (b) 1 (c) 2 (d) 17
  16. 16.What is the smallest prime factor of 115? (a) 1 (b) 23 (c) 2 (d) 5
  17. 17.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 8 (d) 9
  18. 18.How many factors does 114 have? (a) 7 (b) 9 (c) 6 (d) 8
  19. 19.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7² (d) 2³ × 3² × 7
  20. 20.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 23 (d) 7
  21. 21.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5³
  22. 22.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 4 (d) 6
  23. 23.How many factors does 118 have? (a) 4 (b) 5 (c) 3 (d) 2
  24. 24.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
  25. 25.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  26. 26.What is the smallest prime factor of 253? (a) 1 (b) 2 (c) 11 (d) 23
  27. 27.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3³ (c) 2 × 3² (d) 2² × 3²
  28. 28.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  29. 29.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7 (c) 3² × 7 (d) 3 × 7²
  30. 30.What is the smallest prime factor of 93? (a) 1 (b) 31 (c) 2 (d) 3
  31. 31.How many factors does 110 have? (a) 6 (b) 8 (c) 9 (d) 7
  32. 32.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2 × 3 × 5
  33. 33.What is the prime factorisation of 12? (a) 2² × 3 (b) 2 × 3² (c) 2³ × 3 (d) 2 × 3
  34. 34.What is the smallest prime factor of 57? (a) 19 (b) 2 (c) 3 (d) 1
  35. 35.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2³ × 3 (c) 2⁴ × 3 (d) 2² × 3
  36. 36.How many factors does 16 have? (a) 4 (b) 6 (c) 5 (d) 3
  37. 37.What is the smallest prime factor of 319? (a) 2 (b) 11 (c) 1 (d) 29
  38. 38.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
  39. 39.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
  40. 40.How many prime numbers are there between 20 and 50? (a) 7 (b) 8 (c) 9 (d) 6

Answer key

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

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