← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 8 · 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 smallest prime factor of 155? (a) 31 (b) 2 (c) 1 (d) 5
  2. 2.How many factors does 98 have? (a) 5 (b) 4 (c) 6 (d) 7
  3. 3.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 5 (d) 3
  4. 4.How many factors does 77 have? (a) 3 (b) 4 (c) 5 (d) 2
  5. 5.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3² (c) 2³ × 3² (d) 2² × 3³
  6. 6.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 3 (d) 2
  7. 7.How many factors does 17 have? (a) 3 (b) 4 (c) 1 (d) 2
  8. 8.How many factors does 109 have? (a) 1 (b) 4 (c) 2 (d) 3
  9. 9.What is the prime factorisation of 15? (a) 3 × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3² × 5
  10. 10.What is the prime factorisation of 21? (a) 3 × 7² (b) 3 × 7 (c) 3² × 7 (d) 3³ × 7
  11. 11.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 13 (d) 23
  12. 12.What is the smallest prime factor of 319? (a) 29 (b) 1 (c) 11 (d) 2
  13. 13.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2 × 3² × 5³ (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
  14. 14.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 3 (d) 5
  15. 15.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 2 (d) 4
  16. 16.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 4 (d) 3
  17. 17.What is the smallest prime factor of 341? (a) 11 (b) 1 (c) 2 (d) 31
  18. 18.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
  19. 19.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  20. 20.How many factors does 102 have? (a) 8 (b) 6 (c) 7 (d) 9
  21. 21.What is the smallest prime factor of 69? (a) 3 (b) 1 (c) 23 (d) 2
  22. 22.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 9 (d) 8
  23. 23.What is the smallest prime factor of 121? (a) 11 (b) 3 (c) 1 (d) 2
  24. 24.How many factors does 19 have? (a) 2 (b) 3 (c) 1 (d) 4
  25. 25.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
  26. 26.What is the smallest prime factor of 115? (a) 2 (b) 1 (c) 23 (d) 5
  27. 27.What is the smallest prime factor of 209? (a) 11 (b) 19 (c) 2 (d) 1
  28. 28.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 2 (d) 11
  29. 29.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2⁵ × 5 × 7 (d) 2³ × 5 × 7
  30. 30.How many factors does 67 have? (a) 1 (b) 2 (c) 3 (d) 4
  31. 31.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁵ × 3 × 7
  32. 32.How many factors does 107 have? (a) 4 (b) 3 (c) 2 (d) 1
  33. 33.How many factors does 12 have? (a) 6 (b) 7 (c) 5 (d) 4
  34. 34.How many prime numbers are there between 60 and 80? (a) 4 (b) 5 (c) 6 (d) 7
  35. 35.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  36. 36.How many factors does 40 have? (a) 6 (b) 9 (c) 7 (d) 8
  37. 37.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  38. 38.What is the smallest prime factor of 39? (a) 1 (b) 2 (c) 13 (d) 3
  39. 39.What is the smallest prime factor of 161? (a) 7 (b) 23 (c) 1 (d) 2
  40. 40.What is the smallest prime factor of 403? (a) 1 (b) 13 (c) 31 (d) 2

Answer key

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

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