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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 175 · 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 403? (a) 2 (b) 31 (c) 13 (d) 1
  2. 2.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 4 (d) 3
  3. 3.How many factors does 38 have? (a) 3 (b) 4 (c) 2 (d) 5
  4. 4.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5
  5. 5.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2² × 3 × 7
  6. 6.How many prime numbers are there between 10 and 30? (a) 5 (b) 6 (c) 8 (d) 7
  7. 7.What is the prime factorisation of 24? (a) 2² × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3³
  8. 8.What is the prime factorisation of 14? (a) 2 × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2² × 7
  9. 9.What is the prime factorisation of 18? (a) 2² × 3 (b) 2² × 3² (c) 2 × 3³ (d) 2 × 3²
  10. 10.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 2 (d) 1
  11. 11.What is the prime factorisation of 72? (a) 2² × 3² (b) 2⁴ × 3² (c) 2³ × 3² (d) 2² × 3³
  12. 12.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 4 (d) 6
  13. 13.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2² × 3⁴ (c) 2³ × 3² (d) 2⁵ × 3²
  14. 14.How many prime numbers are there between 90 and 110? (a) 4 (b) 7 (c) 6 (d) 5
  15. 15.How many factors does 67 have? (a) 1 (b) 4 (c) 3 (d) 2
  16. 16.How many factors does 42 have? (a) 9 (b) 7 (c) 8 (d) 6
  17. 17.How many factors does 49 have? (a) 4 (b) 3 (c) 2 (d) 1
  18. 18.What is the smallest prime factor of 155? (a) 2 (b) 5 (c) 1 (d) 31
  19. 19.What is the smallest prime factor of 69? (a) 1 (b) 2 (c) 3 (d) 23
  20. 20.What is the prime factorisation of 36? (a) 2² × 3² (b) 2³ × 3² (c) 2 × 3² (d) 2² × 3³
  21. 21.How many factors does 26 have? (a) 4 (b) 5 (c) 3 (d) 2
  22. 22.How many factors does 45 have? (a) 7 (b) 4 (c) 6 (d) 5
  23. 23.How many factors does 119 have? (a) 3 (b) 4 (c) 2 (d) 5
  24. 24.How many factors does 63 have? (a) 7 (b) 6 (c) 5 (d) 4
  25. 25.How many factors does 14 have? (a) 2 (b) 4 (c) 3 (d) 5
  26. 26.How many factors does 64 have? (a) 7 (b) 6 (c) 8 (d) 5
  27. 27.How many factors does 75 have? (a) 6 (b) 7 (c) 5 (d) 4
  28. 28.How many factors does 109 have? (a) 4 (b) 2 (c) 3 (d) 1
  29. 29.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  30. 30.How many factors does 93 have? (a) 4 (b) 2 (c) 3 (d) 5
  31. 31.How many prime numbers are there between 50 and 70? (a) 5 (b) 4 (c) 6 (d) 3
  32. 32.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 2 (d) 1
  33. 33.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 11 (d) 1
  34. 34.How many factors does 70 have? (a) 7 (b) 9 (c) 6 (d) 8
  35. 35.How many factors does 108 have? (a) 11 (b) 13 (c) 10 (d) 12
  36. 36.How many factors does 52 have? (a) 5 (b) 7 (c) 4 (d) 6
  37. 37.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 5 (d) 8
  38. 38.What is the smallest prime factor of 95? (a) 2 (b) 19 (c) 5 (d) 1
  39. 39.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 1 (d) 3
  40. 40.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1

Answer key

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

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