← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 46 · 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 20 and 50? (a) 7 (b) 9 (c) 6 (d) 8
  2. 2.What is the smallest prime factor of 341? (a) 1 (b) 31 (c) 2 (d) 11
  3. 3.What is the smallest prime factor of 299? (a) 2 (b) 23 (c) 13 (d) 1
  4. 4.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3 × 5 × 7
  5. 5.How many factors does 99 have? (a) 7 (b) 5 (c) 4 (d) 6
  6. 6.How many factors does 100 have? (a) 7 (b) 8 (c) 10 (d) 9
  7. 7.What is the smallest prime factor of 247? (a) 2 (b) 19 (c) 1 (d) 13
  8. 8.What is the smallest prime factor of 221? (a) 1 (b) 2 (c) 17 (d) 13
  9. 9.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 31 (d) 7
  10. 10.How many factors does 61 have? (a) 3 (b) 1 (c) 4 (d) 2
  11. 11.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2 × 3² (c) 2² × 3 (d) 2² × 3²
  12. 12.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2³ × 3
  13. 13.How many factors does 75 have? (a) 4 (b) 5 (c) 6 (d) 7
  14. 14.What is the smallest prime factor of 377? (a) 29 (b) 2 (c) 1 (d) 13
  15. 15.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 4 (d) 1
  16. 16.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5³
  17. 17.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 29 (d) 2
  18. 18.What is the smallest prime factor of 51? (a) 3 (b) 2 (c) 1 (d) 17
  19. 19.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 4 (d) 3
  20. 20.How many prime numbers are there between 90 and 100? (a) 2 (b) 1 (c) 3 (d) 0
  21. 21.What is the smallest prime factor of 253? (a) 2 (b) 11 (c) 1 (d) 23
  22. 22.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 1 (d) 3
  23. 23.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 8 (d) 7
  24. 24.How many factors does 120 have? (a) 14 (b) 15 (c) 17 (d) 16
  25. 25.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 3 (d) 2
  26. 26.How many factors does 83 have? (a) 1 (b) 2 (c) 4 (d) 3
  27. 27.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7² (d) 2 × 7
  28. 28.What is the smallest prime factor of 55? (a) 2 (b) 11 (c) 1 (d) 5
  29. 29.What is the prime factorisation of 45? (a) 3 × 5² (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5
  30. 30.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 3 (d) 1
  31. 31.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7 (c) 5 × 7² (d) 5³ × 7
  32. 32.What is the smallest prime factor of 93? (a) 2 (b) 1 (c) 31 (d) 3
  33. 33.How many factors does 76 have? (a) 6 (b) 7 (c) 4 (d) 5
  34. 34.How many factors does 67 have? (a) 1 (b) 3 (c) 4 (d) 2
  35. 35.What is the smallest prime factor of 169? (a) 13 (b) 2 (c) 3 (d) 1
  36. 36.How many factors does 103 have? (a) 3 (b) 1 (c) 4 (d) 2
  37. 37.How many factors does 18 have? (a) 7 (b) 5 (c) 6 (d) 4
  38. 38.What is the smallest prime factor of 95? (a) 1 (b) 19 (c) 2 (d) 5
  39. 39.How many factors does 114 have? (a) 9 (b) 6 (c) 8 (d) 7
  40. 40.How many prime numbers are there between 90 and 120? (a) 6 (b) 8 (c) 5 (d) 7

Answer key

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

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