← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 180 · 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.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 2 (d) 4
  2. 2.How many factors does 83 have? (a) 3 (b) 2 (c) 4 (d) 1
  3. 3.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 5 (d) 1
  4. 4.How many factors does 117 have? (a) 7 (b) 5 (c) 4 (d) 6
  5. 5.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2 × 3² (c) 2 × 3 (d) 2² × 3
  6. 6.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 3 (d) 4
  7. 7.What is the prime factorisation of 18? (a) 2 × 3² (b) 2² × 3 (c) 2² × 3² (d) 2 × 3³
  8. 8.What is the smallest prime factor of 49? (a) 1 (b) 3 (c) 2 (d) 7
  9. 9.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2² × 7
  10. 10.How many factors does 108 have? (a) 10 (b) 11 (c) 13 (d) 12
  11. 11.How many prime numbers are there between 40 and 50? (a) 2 (b) 3 (c) 5 (d) 4
  12. 12.How many factors does 37 have? (a) 3 (b) 2 (c) 4 (d) 1
  13. 13.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 1 (d) 3
  14. 14.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 1 (d) 11
  15. 15.What is the smallest prime factor of 217? (a) 2 (b) 7 (c) 31 (d) 1
  16. 16.What is the smallest prime factor of 21? (a) 2 (b) 1 (c) 3 (d) 7
  17. 17.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 1 (d) 2
  18. 18.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  19. 19.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7³ (d) 2⁴ × 7
  20. 20.How many factors does 58 have? (a) 2 (b) 3 (c) 5 (d) 4
  21. 21.How many factors does 93 have? (a) 3 (b) 2 (c) 5 (d) 4
  22. 22.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
  23. 23.What is the smallest prime factor of 119? (a) 17 (b) 7 (c) 1 (d) 2
  24. 24.How many factors does 21 have? (a) 3 (b) 4 (c) 2 (d) 5
  25. 25.How many prime numbers are there between 20 and 50? (a) 7 (b) 9 (c) 8 (d) 6
  26. 26.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3³ (d) 2⁴ × 3
  27. 27.What is the smallest prime factor of 319? (a) 1 (b) 11 (c) 2 (d) 29
  28. 28.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3³ × 5 (d) 3² × 5
  29. 29.What is the smallest prime factor of 403? (a) 2 (b) 31 (c) 13 (d) 1
  30. 30.How many factors does 92 have? (a) 5 (b) 6 (c) 4 (d) 7
  31. 31.How many factors does 41 have? (a) 3 (b) 2 (c) 4 (d) 1
  32. 32.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  33. 33.What is the smallest prime factor of 145? (a) 2 (b) 29 (c) 5 (d) 1
  34. 34.How many factors does 74 have? (a) 5 (b) 3 (c) 4 (d) 2
  35. 35.How many prime numbers are there between 40 and 60? (a) 7 (b) 6 (c) 5 (d) 4
  36. 36.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  37. 37.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 2 (d) 29
  38. 38.How many factors does 56 have? (a) 7 (b) 6 (c) 9 (d) 8
  39. 39.How many factors does 12 have? (a) 5 (b) 6 (c) 4 (d) 7
  40. 40.How many factors does 26 have? (a) 4 (b) 5 (c) 3 (d) 2

Answer key

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

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