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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 192 · 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 113 have? (a) 1 (b) 3 (c) 2 (d) 4
  2. 2.What is the smallest prime factor of 253? (a) 23 (b) 2 (c) 1 (d) 11
  3. 3.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 3 (d) 2
  4. 4.How many factors does 37 have? (a) 2 (b) 1 (c) 3 (d) 4
  5. 5.What is the smallest prime factor of 95? (a) 1 (b) 5 (c) 19 (d) 2
  6. 6.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2² × 5 × 7
  7. 7.What is the smallest prime factor of 247? (a) 2 (b) 13 (c) 19 (d) 1
  8. 8.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 1 (d) 11
  9. 9.How many factors does 31 have? (a) 1 (b) 3 (c) 2 (d) 4
  10. 10.How many prime numbers are there between 80 and 90? (a) 2 (b) 4 (c) 3 (d) 1
  11. 11.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2⁴ × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
  12. 12.How many factors does 53 have? (a) 4 (b) 2 (c) 3 (d) 1
  13. 13.What is the smallest prime factor of 299? (a) 2 (b) 23 (c) 1 (d) 13
  14. 14.How many factors does 95 have? (a) 2 (b) 3 (c) 5 (d) 4
  15. 15.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5³
  16. 16.How many prime numbers are there between 70 and 80? (a) 5 (b) 3 (c) 4 (d) 2
  17. 17.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 2 (d) 13
  18. 18.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2² × 3² × 5
  19. 19.How many factors does 69 have? (a) 5 (b) 4 (c) 2 (d) 3
  20. 20.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 3 (d) 4
  21. 21.How many prime numbers are there between 50 and 80? (a) 7 (b) 6 (c) 9 (d) 8
  22. 22.What is the smallest prime factor of 377? (a) 29 (b) 13 (c) 1 (d) 2
  23. 23.What is the smallest prime factor of 55? (a) 11 (b) 2 (c) 5 (d) 1
  24. 24.How many factors does 19 have? (a) 3 (b) 4 (c) 1 (d) 2
  25. 25.What is the smallest prime factor of 133? (a) 7 (b) 2 (c) 19 (d) 1
  26. 26.How many factors does 57 have? (a) 2 (b) 4 (c) 5 (d) 3
  27. 27.How many factors does 118 have? (a) 3 (b) 2 (c) 5 (d) 4
  28. 28.What is the smallest prime factor of 155? (a) 2 (b) 5 (c) 1 (d) 31
  29. 29.What is the prime factorisation of 36? (a) 2² × 3² (b) 2 × 3² (c) 2³ × 3² (d) 2² × 3³
  30. 30.How many factors does 74 have? (a) 3 (b) 4 (c) 5 (d) 2
  31. 31.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
  32. 32.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2⁴ × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7³
  33. 33.What is the smallest prime factor of 143? (a) 2 (b) 11 (c) 1 (d) 13
  34. 34.How many factors does 71 have? (a) 3 (b) 1 (c) 4 (d) 2
  35. 35.How many factors does 49 have? (a) 4 (b) 2 (c) 3 (d) 1
  36. 36.What is the smallest prime factor of 49? (a) 1 (b) 7 (c) 3 (d) 2
  37. 37.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 8 (d) 9
  38. 38.What is the smallest prime factor of 115? (a) 2 (b) 1 (c) 23 (d) 5
  39. 39.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  40. 40.What is the smallest prime factor of 39? (a) 2 (b) 1 (c) 3 (d) 13

Answer key

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

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