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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 112 · 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 prime factorisation of 72? (a) 2² × 3² (b) 2⁴ × 3² (c) 2³ × 3² (d) 2² × 3³
  2. 2.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 1 (d) 0
  3. 3.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
  4. 4.How many prime numbers are there between 50 and 60? (a) 2 (b) 1 (c) 3 (d) 4
  5. 5.How many prime numbers are there between 50 and 70? (a) 4 (b) 6 (c) 5 (d) 3
  6. 6.What is the smallest prime factor of 87? (a) 2 (b) 3 (c) 29 (d) 1
  7. 7.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2 × 3² (c) 2² × 3³ (d) 2² × 3²
  8. 8.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 7 (d) 4
  9. 9.What is the smallest prime factor of 377? (a) 1 (b) 2 (c) 29 (d) 13
  10. 10.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 13 (d) 1
  11. 11.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  12. 12.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 9 (d) 7
  13. 13.How many factors does 33 have? (a) 4 (b) 2 (c) 5 (d) 3
  14. 14.What is the smallest prime factor of 155? (a) 2 (b) 31 (c) 1 (d) 5
  15. 15.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 1 (d) 11
  16. 16.How many prime numbers are there between 60 and 90? (a) 9 (b) 6 (c) 8 (d) 7
  17. 17.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  18. 18.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
  19. 19.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 2 (d) 3
  20. 20.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 8 (d) 7
  21. 21.How many factors does 105 have? (a) 9 (b) 7 (c) 8 (d) 6
  22. 22.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
  23. 23.How many factors does 65 have? (a) 2 (b) 4 (c) 5 (d) 3
  24. 24.What is the smallest prime factor of 91? (a) 7 (b) 13 (c) 1 (d) 2
  25. 25.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
  26. 26.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 7 (d) 9
  27. 27.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5
  28. 28.How many factors does 74 have? (a) 3 (b) 2 (c) 5 (d) 4
  29. 29.How many factors does 36 have? (a) 7 (b) 9 (c) 8 (d) 10
  30. 30.How many factors does 40 have? (a) 7 (b) 6 (c) 8 (d) 9
  31. 31.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  32. 32.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 5 (d) 4
  33. 33.How many factors does 87 have? (a) 2 (b) 4 (c) 3 (d) 5
  34. 34.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 2 (d) 5
  35. 35.How many factors does 35 have? (a) 5 (b) 4 (c) 3 (d) 2
  36. 36.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  37. 37.How many factors does 27 have? (a) 3 (b) 4 (c) 2 (d) 5
  38. 38.How many factors does 59 have? (a) 3 (b) 4 (c) 1 (d) 2
  39. 39.What is the smallest prime factor of 319? (a) 1 (b) 29 (c) 2 (d) 11
  40. 40.How many factors does 107 have? (a) 2 (b) 3 (c) 4 (d) 1

Answer key

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

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