← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 69 · 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 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  2. 2.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2² × 5 (c) 2 × 5³ (d) 2³ × 5
  3. 3.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 2 (d) 11
  4. 4.What is the smallest prime factor of 119? (a) 1 (b) 7 (c) 17 (d) 2
  5. 5.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2⁴ × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  6. 6.How many factors does 113 have? (a) 3 (b) 1 (c) 2 (d) 4
  7. 7.How many prime numbers are there between 90 and 110? (a) 6 (b) 7 (c) 4 (d) 5
  8. 8.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
  9. 9.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2³ × 3² × 5
  10. 10.What is the smallest prime factor of 69? (a) 3 (b) 23 (c) 2 (d) 1
  11. 11.How many factors does 107 have? (a) 2 (b) 3 (c) 4 (d) 1
  12. 12.How many factors does 38 have? (a) 5 (b) 4 (c) 3 (d) 2
  13. 13.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
  14. 14.How many factors does 102 have? (a) 6 (b) 9 (c) 8 (d) 7
  15. 15.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 7 (d) 2
  16. 16.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 5 (d) 3
  17. 17.What is the prime factorisation of 18? (a) 2 × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2² × 3²
  18. 18.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 3 (d) 2
  19. 19.How many factors does 93 have? (a) 4 (b) 3 (c) 5 (d) 2
  20. 20.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 5 (d) 7
  21. 21.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3² × 5 × 7
  22. 22.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  23. 23.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  24. 24.How many factors does 114 have? (a) 6 (b) 9 (c) 8 (d) 7
  25. 25.How many prime numbers are there between 90 and 120? (a) 5 (b) 8 (c) 6 (d) 7
  26. 26.How many factors does 117 have? (a) 7 (b) 5 (c) 6 (d) 4
  27. 27.How many factors does 111 have? (a) 4 (b) 2 (c) 3 (d) 5
  28. 28.What is the smallest prime factor of 299? (a) 1 (b) 13 (c) 23 (d) 2
  29. 29.What is the smallest prime factor of 247? (a) 2 (b) 13 (c) 1 (d) 19
  30. 30.How many factors does 118 have? (a) 5 (b) 3 (c) 4 (d) 2
  31. 31.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 1 (d) 2
  32. 32.How many prime numbers are there between 10 and 40? (a) 10 (b) 8 (c) 7 (d) 9
  33. 33.How many factors does 49 have? (a) 1 (b) 3 (c) 4 (d) 2
  34. 34.How many factors does 26 have? (a) 2 (b) 5 (c) 3 (d) 4
  35. 35.How many prime numbers are there between 70 and 90? (a) 6 (b) 4 (c) 5 (d) 7
  36. 36.How many factors does 21 have? (a) 3 (b) 2 (c) 5 (d) 4
  37. 37.How many factors does 61 have? (a) 4 (b) 2 (c) 3 (d) 1
  38. 38.What is the smallest prime factor of 21? (a) 2 (b) 1 (c) 3 (d) 7
  39. 39.What is the prime factorisation of 12? (a) 2 × 3² (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3
  40. 40.What is the smallest prime factor of 49? (a) 1 (b) 3 (c) 7 (d) 2

Answer key

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

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