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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 138 · 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 77? (a) 11 (b) 2 (c) 1 (d) 7
  2. 2.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2
  3. 3.What is the smallest prime factor of 39? (a) 13 (b) 1 (c) 3 (d) 2
  4. 4.How many factors does 22 have? (a) 5 (b) 3 (c) 2 (d) 4
  5. 5.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 4 (d) 5
  6. 6.How many factors does 24 have? (a) 6 (b) 7 (c) 8 (d) 9
  7. 7.How many factors does 57 have? (a) 5 (b) 4 (c) 2 (d) 3
  8. 8.How many factors does 42 have? (a) 6 (b) 7 (c) 8 (d) 9
  9. 9.How many prime numbers are there between 60 and 70? (a) 1 (b) 3 (c) 4 (d) 2
  10. 10.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2³ × 3²
  11. 11.What is the smallest prime factor of 55? (a) 5 (b) 11 (c) 1 (d) 2
  12. 12.What is the prime factorisation of 35? (a) 5² × 7 (b) 5³ × 7 (c) 5 × 7 (d) 5 × 7²
  13. 13.What is the smallest prime factor of 35? (a) 1 (b) 2 (c) 5 (d) 7
  14. 14.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 4 (d) 6
  15. 15.What is the smallest prime factor of 57? (a) 3 (b) 1 (c) 19 (d) 2
  16. 16.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2 × 7⁴ (c) 2³ × 7 (d) 2⁴ × 7
  17. 17.How many factors does 67 have? (a) 4 (b) 1 (c) 3 (d) 2
  18. 18.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 3 (d) 5
  19. 19.What is the smallest prime factor of 119? (a) 7 (b) 2 (c) 17 (d) 1
  20. 20.How many prime numbers are there between 80 and 100? (a) 2 (b) 4 (c) 5 (d) 3
  21. 21.How many factors does 107 have? (a) 2 (b) 4 (c) 1 (d) 3
  22. 22.How many prime numbers are there between 80 and 110? (a) 9 (b) 6 (c) 7 (d) 8
  23. 23.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5³
  24. 24.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 7 (d) 5
  25. 25.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5³ (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  26. 26.How many factors does 32 have? (a) 5 (b) 4 (c) 6 (d) 7
  27. 27.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
  28. 28.How many factors does 59 have? (a) 3 (b) 2 (c) 4 (d) 1
  29. 29.How many factors does 115 have? (a) 2 (b) 4 (c) 3 (d) 5
  30. 30.How many factors does 74 have? (a) 4 (b) 2 (c) 3 (d) 5
  31. 31.How many factors does 111 have? (a) 3 (b) 4 (c) 2 (d) 5
  32. 32.How many factors does 19 have? (a) 4 (b) 1 (c) 3 (d) 2
  33. 33.How many factors does 21 have? (a) 3 (b) 2 (c) 5 (d) 4
  34. 34.What is the smallest prime factor of 85? (a) 1 (b) 5 (c) 2 (d) 17
  35. 35.How many factors does 101 have? (a) 1 (b) 3 (c) 4 (d) 2
  36. 36.How many factors does 80 have? (a) 11 (b) 8 (c) 9 (d) 10
  37. 37.What is the smallest prime factor of 161? (a) 23 (b) 7 (c) 1 (d) 2
  38. 38.How many factors does 62 have? (a) 2 (b) 5 (c) 3 (d) 4
  39. 39.What is the smallest prime factor of 221? (a) 13 (b) 17 (c) 1 (d) 2
  40. 40.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2³ × 5 × 7

Answer key

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

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