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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 99 · 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 × 3³ (b) 2² × 3² (c) 2⁴ × 3² (d) 2³ × 3²
  2. 2.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
  3. 3.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  4. 4.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 3 (d) 1
  5. 5.How many prime numbers are there between 60 and 80? (a) 5 (b) 4 (c) 6 (d) 7
  6. 6.How many factors does 96 have? (a) 13 (b) 11 (c) 10 (d) 12
  7. 7.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
  8. 8.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 7 (d) 11
  9. 9.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  10. 10.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 6 (d) 7
  11. 11.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 6 (d) 5
  12. 12.How many prime numbers are there between 60 and 70? (a) 2 (b) 4 (c) 3 (d) 1
  13. 13.What is the prime factorisation of 20? (a) 2 × 5² (b) 2³ × 5 (c) 2 × 5 (d) 2² × 5
  14. 14.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  15. 15.What is the smallest prime factor of 57? (a) 2 (b) 1 (c) 3 (d) 19
  16. 16.How many factors does 18 have? (a) 6 (b) 4 (c) 5 (d) 7
  17. 17.What is the smallest prime factor of 299? (a) 23 (b) 1 (c) 13 (d) 2
  18. 18.How many factors does 71 have? (a) 1 (b) 2 (c) 4 (d) 3
  19. 19.How many factors does 62 have? (a) 3 (b) 2 (c) 5 (d) 4
  20. 20.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
  21. 21.How many factors does 28 have? (a) 6 (b) 5 (c) 4 (d) 7
  22. 22.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7² (d) 2³ × 3² × 7
  23. 23.How many prime numbers are there between 80 and 90? (a) 4 (b) 1 (c) 2 (d) 3
  24. 24.What is the smallest prime factor of 203? (a) 29 (b) 2 (c) 7 (d) 1
  25. 25.How many factors does 87 have? (a) 4 (b) 2 (c) 5 (d) 3
  26. 26.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 4 (d) 5
  27. 27.What is the smallest prime factor of 33? (a) 2 (b) 1 (c) 3 (d) 11
  28. 28.What is the smallest prime factor of 403? (a) 2 (b) 31 (c) 1 (d) 13
  29. 29.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 17 (d) 2
  30. 30.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 2 (d) 11
  31. 31.How many factors does 57 have? (a) 2 (b) 3 (c) 4 (d) 5
  32. 32.How many factors does 119 have? (a) 2 (b) 5 (c) 4 (d) 3
  33. 33.What is the smallest prime factor of 341? (a) 11 (b) 1 (c) 31 (d) 2
  34. 34.How many factors does 16 have? (a) 6 (b) 5 (c) 3 (d) 4
  35. 35.How many factors does 79 have? (a) 4 (b) 2 (c) 1 (d) 3
  36. 36.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3 × 7 (d) 3² × 7
  37. 37.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2 × 3⁴ (c) 2³ × 3 (d) 2⁴ × 3
  38. 38.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁵ × 5 (d) 2⁴ × 5
  39. 39.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
  40. 40.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2² × 5 × 7

Answer key

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

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