← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 123 · 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 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3² × 5 × 7
  2. 2.How many prime numbers are there between 60 and 90? (a) 7 (b) 9 (c) 8 (d) 6
  3. 3.How many factors does 82 have? (a) 2 (b) 4 (c) 3 (d) 5
  4. 4.How many factors does 93 have? (a) 3 (b) 5 (c) 4 (d) 2
  5. 5.How many factors does 70 have? (a) 6 (b) 7 (c) 8 (d) 9
  6. 6.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 6 (d) 7
  7. 7.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2² × 7
  8. 8.What is the smallest prime factor of 115? (a) 1 (b) 2 (c) 5 (d) 23
  9. 9.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  10. 10.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  11. 11.What is the smallest prime factor of 39? (a) 1 (b) 2 (c) 13 (d) 3
  12. 12.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
  13. 13.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 4 (d) 3
  14. 14.How many prime numbers are there between 20 and 40? (a) 6 (b) 4 (c) 3 (d) 5
  15. 15.How many prime numbers are there between 60 and 70? (a) 1 (b) 4 (c) 2 (d) 3
  16. 16.What is the smallest prime factor of 187? (a) 2 (b) 11 (c) 17 (d) 1
  17. 17.How many factors does 40 have? (a) 6 (b) 7 (c) 9 (d) 8
  18. 18.How many factors does 107 have? (a) 3 (b) 2 (c) 1 (d) 4
  19. 19.How many factors does 28 have? (a) 7 (b) 4 (c) 6 (d) 5
  20. 20.How many factors does 120 have? (a) 17 (b) 16 (c) 15 (d) 14
  21. 21.What is the prime factorisation of 12? (a) 2 × 3² (b) 2 × 3 (c) 2³ × 3 (d) 2² × 3
  22. 22.How many factors does 22 have? (a) 2 (b) 5 (c) 3 (d) 4
  23. 23.What is the smallest prime factor of 169? (a) 1 (b) 13 (c) 2 (d) 3
  24. 24.How many factors does 78 have? (a) 6 (b) 8 (c) 7 (d) 9
  25. 25.How many factors does 104 have? (a) 8 (b) 6 (c) 9 (d) 7
  26. 26.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  27. 27.How many factors does 101 have? (a) 2 (b) 1 (c) 4 (d) 3
  28. 28.How many factors does 118 have? (a) 3 (b) 4 (c) 2 (d) 5
  29. 29.What is the smallest prime factor of 253? (a) 23 (b) 11 (c) 1 (d) 2
  30. 30.How many factors does 86 have? (a) 5 (b) 4 (c) 3 (d) 2
  31. 31.How many factors does 18 have? (a) 5 (b) 6 (c) 4 (d) 7
  32. 32.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
  33. 33.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
  34. 34.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2 × 3² (c) 2² × 3² (d) 2² × 3
  35. 35.How many factors does 103 have? (a) 2 (b) 1 (c) 3 (d) 4
  36. 36.How many factors does 45 have? (a) 6 (b) 4 (c) 5 (d) 7
  37. 37.How many factors does 61 have? (a) 2 (b) 1 (c) 4 (d) 3
  38. 38.How many factors does 80 have? (a) 8 (b) 11 (c) 10 (d) 9
  39. 39.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 6 (d) 7
  40. 40.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8

Answer key

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

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