← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 50 · 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 40 and 50? (a) 3 (b) 5 (c) 2 (d) 4
  2. 2.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 6 (d) 5
  3. 3.How many factors does 105 have? (a) 6 (b) 8 (c) 9 (d) 7
  4. 4.How many factors does 74 have? (a) 5 (b) 3 (c) 2 (d) 4
  5. 5.How many prime numbers are there between 20 and 40? (a) 6 (b) 4 (c) 3 (d) 5
  6. 6.How many prime numbers are there between 60 and 70? (a) 1 (b) 4 (c) 2 (d) 3
  7. 7.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
  8. 8.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 9 (d) 7
  9. 9.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 5 (d) 4
  10. 10.What is the smallest prime factor of 155? (a) 5 (b) 31 (c) 2 (d) 1
  11. 11.What is the prime factorisation of 15? (a) 3 × 5² (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5
  12. 12.How many factors does 86 have? (a) 2 (b) 4 (c) 3 (d) 5
  13. 13.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2 × 5 × 7 (d) 2² × 5 × 7
  14. 14.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
  15. 15.What is the smallest prime factor of 145? (a) 1 (b) 5 (c) 29 (d) 2
  16. 16.How many factors does 33 have? (a) 4 (b) 2 (c) 5 (d) 3
  17. 17.How many factors does 104 have? (a) 7 (b) 9 (c) 8 (d) 6
  18. 18.How many prime numbers are there between 10 and 40? (a) 8 (b) 7 (c) 10 (d) 9
  19. 19.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2² × 3² (d) 2 × 3²
  20. 20.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 13 (d) 5
  21. 21.How many factors does 101 have? (a) 3 (b) 4 (c) 1 (d) 2
  22. 22.How many factors does 85 have? (a) 4 (b) 5 (c) 3 (d) 2
  23. 23.How many factors does 87 have? (a) 3 (b) 2 (c) 4 (d) 5
  24. 24.What is the smallest prime factor of 403? (a) 2 (b) 13 (c) 31 (d) 1
  25. 25.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2
  26. 26.How many factors does 93 have? (a) 3 (b) 5 (c) 4 (d) 2
  27. 27.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
  28. 28.How many factors does 100 have? (a) 9 (b) 10 (c) 8 (d) 7
  29. 29.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 7 (d) 1
  30. 30.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5² (d) 2³ × 3² × 5
  31. 31.How many factors does 59 have? (a) 2 (b) 1 (c) 4 (d) 3
  32. 32.What is the smallest prime factor of 57? (a) 19 (b) 2 (c) 1 (d) 3
  33. 33.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
  34. 34.How many factors does 27 have? (a) 2 (b) 4 (c) 3 (d) 5
  35. 35.How many factors does 47 have? (a) 3 (b) 4 (c) 1 (d) 2
  36. 36.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  37. 37.What is the smallest prime factor of 209? (a) 19 (b) 11 (c) 1 (d) 2
  38. 38.What is the smallest prime factor of 93? (a) 3 (b) 31 (c) 2 (d) 1
  39. 39.How many factors does 41 have? (a) 4 (b) 3 (c) 1 (d) 2
  40. 40.How many prime numbers are there between 90 and 100? (a) 3 (b) 1 (c) 0 (d) 2

Answer key

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

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