← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 5 · 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 560? (a) 2 × 5 × 7⁴ (b) 2⁵ × 5 × 7 (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
  2. 2.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 4 (d) 5
  3. 3.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  4. 4.How many factors does 66 have? (a) 6 (b) 9 (c) 7 (d) 8
  5. 5.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 1 (d) 7
  6. 6.How many factors does 71 have? (a) 3 (b) 1 (c) 4 (d) 2
  7. 7.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 11 (d) 1
  8. 8.What is the smallest prime factor of 119? (a) 17 (b) 1 (c) 7 (d) 2
  9. 9.How many prime numbers are there between 70 and 90? (a) 6 (b) 4 (c) 7 (d) 5
  10. 10.How many prime numbers are there between 30 and 50? (a) 5 (b) 4 (c) 7 (d) 6
  11. 11.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 29 (d) 11
  12. 12.How many factors does 18 have? (a) 5 (b) 4 (c) 7 (d) 6
  13. 13.How many factors does 40 have? (a) 8 (b) 9 (c) 7 (d) 6
  14. 14.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2 × 5 × 7
  15. 15.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2 × 3² × 7
  16. 16.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 6 (d) 4
  17. 17.How many factors does 19 have? (a) 2 (b) 4 (c) 3 (d) 1
  18. 18.How many factors does 29 have? (a) 3 (b) 2 (c) 4 (d) 1
  19. 19.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 3 (d) 1
  20. 20.What is the smallest prime factor of 35? (a) 1 (b) 5 (c) 7 (d) 2
  21. 21.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2² × 5 (c) 2 × 5 (d) 2 × 5²
  22. 22.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 2 (d) 1
  23. 23.How many factors does 17 have? (a) 3 (b) 4 (c) 1 (d) 2
  24. 24.What is the prime factorisation of 12? (a) 2 × 3² (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3
  25. 25.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 29 (d) 3
  26. 26.What is the prime factorisation of 24? (a) 2 × 3³ (b) 2³ × 3 (c) 2² × 3 (d) 2⁴ × 3
  27. 27.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 1 (d) 2
  28. 28.What is the prime factorisation of 18? (a) 2² × 3 (b) 2² × 3² (c) 2 × 3² (d) 2 × 3³
  29. 29.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
  30. 30.What is the prime factorisation of 63? (a) 3 × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3² × 7
  31. 31.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2 × 3 × 5
  32. 32.How many factors does 56 have? (a) 7 (b) 6 (c) 8 (d) 9
  33. 33.What is the smallest prime factor of 91? (a) 2 (b) 7 (c) 13 (d) 1
  34. 34.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 2 (d) 5
  35. 35.How many factors does 27 have? (a) 3 (b) 5 (c) 4 (d) 2
  36. 36.How many factors does 107 have? (a) 1 (b) 3 (c) 2 (d) 4
  37. 37.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
  38. 38.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 2 (d) 1
  39. 39.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2 × 3²
  40. 40.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 3 (d) 1

Answer key

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

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad