← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 170 · 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 factors does 13 have? (a) 1 (b) 4 (c) 3 (d) 2
  2. 2.How many factors does 40 have? (a) 9 (b) 7 (c) 6 (d) 8
  3. 3.What is the prime factorisation of 14? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
  4. 4.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2⁵ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁴ × 5 × 7
  5. 5.What is the smallest prime factor of 145? (a) 5 (b) 29 (c) 1 (d) 2
  6. 6.How many factors does 58 have? (a) 2 (b) 5 (c) 3 (d) 4
  7. 7.How many factors does 51 have? (a) 2 (b) 3 (c) 4 (d) 5
  8. 8.What is the smallest prime factor of 93? (a) 2 (b) 31 (c) 1 (d) 3
  9. 9.How many factors does 68 have? (a) 4 (b) 5 (c) 7 (d) 6
  10. 10.How many prime numbers are there between 80 and 100? (a) 3 (b) 4 (c) 2 (d) 5
  11. 11.How many factors does 37 have? (a) 1 (b) 3 (c) 2 (d) 4
  12. 12.What is the smallest prime factor of 85? (a) 5 (b) 1 (c) 2 (d) 17
  13. 13.How many prime numbers are there between 80 and 110? (a) 6 (b) 9 (c) 8 (d) 7
  14. 14.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 5 (d) 2
  15. 15.What is the smallest prime factor of 187? (a) 2 (b) 11 (c) 1 (d) 17
  16. 16.How many factors does 34 have? (a) 5 (b) 4 (c) 3 (d) 2
  17. 17.How many factors does 63 have? (a) 5 (b) 6 (c) 7 (d) 4
  18. 18.How many factors does 20 have? (a) 6 (b) 7 (c) 5 (d) 4
  19. 19.What is the smallest prime factor of 377? (a) 13 (b) 29 (c) 2 (d) 1
  20. 20.How many factors does 25 have? (a) 4 (b) 1 (c) 3 (d) 2
  21. 21.How many factors does 41 have? (a) 2 (b) 1 (c) 4 (d) 3
  22. 22.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 5 (d) 6
  23. 23.What is the smallest prime factor of 253? (a) 11 (b) 1 (c) 23 (d) 2
  24. 24.How many factors does 31 have? (a) 4 (b) 3 (c) 1 (d) 2
  25. 25.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
  26. 26.How many factors does 86 have? (a) 2 (b) 3 (c) 5 (d) 4
  27. 27.What is the smallest prime factor of 133? (a) 19 (b) 1 (c) 2 (d) 7
  28. 28.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 7 (d) 1
  29. 29.How many prime numbers are there between 90 and 110? (a) 6 (b) 5 (c) 7 (d) 4
  30. 30.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
  31. 31.How many factors does 50 have? (a) 7 (b) 5 (c) 4 (d) 6
  32. 32.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  33. 33.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 2 (d) 1
  34. 34.How many factors does 65 have? (a) 3 (b) 2 (c) 5 (d) 4
  35. 35.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 3 (d) 5
  36. 36.How many prime numbers are there between 40 and 70? (a) 6 (b) 9 (c) 7 (d) 8
  37. 37.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 1 (d) 2
  38. 38.What is the smallest prime factor of 65? (a) 5 (b) 2 (c) 1 (d) 13
  39. 39.How many factors does 87 have? (a) 3 (b) 2 (c) 4 (d) 5
  40. 40.How many factors does 70 have? (a) 8 (b) 9 (c) 6 (d) 7

Answer key

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

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