← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 113 · 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 18? (a) 2 × 3³ (b) 2² × 3 (c) 2 × 3² (d) 2² × 3²
  2. 2.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  3. 3.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  4. 4.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
  5. 5.How many prime numbers are there between 60 and 80? (a) 6 (b) 5 (c) 7 (d) 4
  6. 6.What is the prime factorisation of 15? (a) 3 × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3² × 5
  7. 7.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
  8. 8.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 2 (d) 0
  9. 9.What is the smallest prime factor of 133? (a) 19 (b) 7 (c) 1 (d) 2
  10. 10.How many prime numbers are there between 80 and 110? (a) 6 (b) 9 (c) 8 (d) 7
  11. 11.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 5 (d) 3
  12. 12.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  13. 13.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  14. 14.How many factors does 76 have? (a) 4 (b) 6 (c) 7 (d) 5
  15. 15.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2 × 5 × 7⁴
  16. 16.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 29 (d) 3
  17. 17.What is the smallest prime factor of 299? (a) 1 (b) 2 (c) 13 (d) 23
  18. 18.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
  19. 19.How many factors does 21 have? (a) 4 (b) 5 (c) 2 (d) 3
  20. 20.How many factors does 75 have? (a) 4 (b) 5 (c) 6 (d) 7
  21. 21.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 4 (d) 2
  22. 22.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 1 (d) 31
  23. 23.How many prime numbers are there between 60 and 90? (a) 6 (b) 8 (c) 7 (d) 9
  24. 24.How many factors does 31 have? (a) 2 (b) 1 (c) 4 (d) 3
  25. 25.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
  26. 26.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3³
  27. 27.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2⁴ × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  28. 28.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3 × 5
  29. 29.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2² × 3² × 7
  30. 30.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 3 (d) 1
  31. 31.How many factors does 36 have? (a) 8 (b) 9 (c) 7 (d) 10
  32. 32.How many factors does 78 have? (a) 7 (b) 6 (c) 9 (d) 8
  33. 33.How many factors does 61 have? (a) 2 (b) 4 (c) 3 (d) 1
  34. 34.What is the smallest prime factor of 119? (a) 1 (b) 7 (c) 2 (d) 17
  35. 35.What is the smallest prime factor of 95? (a) 19 (b) 1 (c) 2 (d) 5
  36. 36.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 17 (d) 11
  37. 37.What is the smallest prime factor of 209? (a) 2 (b) 1 (c) 11 (d) 19
  38. 38.How many factors does 65 have? (a) 3 (b) 5 (c) 4 (d) 2
  39. 39.How many factors does 46 have? (a) 2 (b) 4 (c) 5 (d) 3
  40. 40.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 1 (d) 7

Answer key

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

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