← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 87 · 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 133? (a) 1 (b) 19 (c) 2 (d) 7
  2. 2.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2 × 5⁴ (c) 2⁵ × 5 (d) 2³ × 5
  3. 3.How many factors does 68 have? (a) 4 (b) 5 (c) 6 (d) 7
  4. 4.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
  5. 5.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  6. 6.How many factors does 94 have? (a) 3 (b) 4 (c) 2 (d) 5
  7. 7.How many factors does 86 have? (a) 5 (b) 2 (c) 3 (d) 4
  8. 8.What is the smallest prime factor of 35? (a) 2 (b) 7 (c) 5 (d) 1
  9. 9.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
  10. 10.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 8 (d) 5
  11. 11.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  12. 12.How many factors does 24 have? (a) 6 (b) 9 (c) 8 (d) 7
  13. 13.What is the smallest prime factor of 217? (a) 7 (b) 1 (c) 2 (d) 31
  14. 14.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  15. 15.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 4 (d) 2
  16. 16.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2² × 5 (c) 2³ × 5 (d) 2⁴ × 5
  17. 17.How many factors does 74 have? (a) 5 (b) 4 (c) 3 (d) 2
  18. 18.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 2 (d) 1
  19. 19.How many factors does 73 have? (a) 4 (b) 1 (c) 3 (d) 2
  20. 20.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2 × 3² (c) 2 × 3 (d) 2² × 3
  21. 21.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  22. 22.How many factors does 13 have? (a) 1 (b) 3 (c) 2 (d) 4
  23. 23.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 1 (d) 3
  24. 24.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
  25. 25.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5 (c) 2³ × 5 (d) 2 × 5²
  26. 26.How many factors does 45 have? (a) 5 (b) 7 (c) 4 (d) 6
  27. 27.How many factors does 43 have? (a) 3 (b) 2 (c) 4 (d) 1
  28. 28.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 3 (d) 4
  29. 29.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
  30. 30.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 2 (d) 17
  31. 31.What is the smallest prime factor of 95? (a) 1 (b) 19 (c) 5 (d) 2
  32. 32.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7
  33. 33.How many factors does 71 have? (a) 4 (b) 3 (c) 2 (d) 1
  34. 34.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 7 (d) 5
  35. 35.How many factors does 101 have? (a) 1 (b) 3 (c) 2 (d) 4
  36. 36.How many factors does 114 have? (a) 7 (b) 8 (c) 6 (d) 9
  37. 37.What is the smallest prime factor of 21? (a) 7 (b) 3 (c) 1 (d) 2
  38. 38.How many factors does 87 have? (a) 2 (b) 5 (c) 4 (d) 3
  39. 39.How many factors does 22 have? (a) 4 (b) 3 (c) 5 (d) 2
  40. 40.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 6 (d) 9

Answer key

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

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