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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 83 · 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 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  2. 2.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 2 (d) 5
  3. 3.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 2 (d) 1
  4. 4.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 4 (d) 6
  5. 5.How many factors does 95 have? (a) 3 (b) 4 (c) 2 (d) 5
  6. 6.What is the smallest prime factor of 39? (a) 3 (b) 2 (c) 13 (d) 1
  7. 7.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 2 (d) 17
  8. 8.What is the smallest prime factor of 203? (a) 2 (b) 7 (c) 1 (d) 29
  9. 9.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2⁵ × 7 (c) 2³ × 7 (d) 2 × 7⁴
  10. 10.How many prime numbers are there between 60 and 70? (a) 4 (b) 3 (c) 2 (d) 1
  11. 11.What is the smallest prime factor of 253? (a) 11 (b) 2 (c) 23 (d) 1
  12. 12.What is the smallest prime factor of 403? (a) 1 (b) 2 (c) 31 (d) 13
  13. 13.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  14. 14.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  15. 15.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 6 (d) 7
  16. 16.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 1 (d) 3
  17. 17.What is the smallest prime factor of 143? (a) 2 (b) 11 (c) 13 (d) 1
  18. 18.How many factors does 52 have? (a) 7 (b) 4 (c) 5 (d) 6
  19. 19.How many prime numbers are there between 60 and 90? (a) 7 (b) 8 (c) 9 (d) 6
  20. 20.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 1 (d) 3
  21. 21.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 2 (d) 3
  22. 22.What is the smallest prime factor of 299? (a) 13 (b) 2 (c) 23 (d) 1
  23. 23.What is the smallest prime factor of 377? (a) 29 (b) 13 (c) 2 (d) 1
  24. 24.How many factors does 104 have? (a) 7 (b) 6 (c) 8 (d) 9
  25. 25.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 7 (d) 2
  26. 26.How many factors does 42 have? (a) 9 (b) 6 (c) 7 (d) 8
  27. 27.How many factors does 85 have? (a) 4 (b) 5 (c) 3 (d) 2
  28. 28.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2⁴ × 5 × 7
  29. 29.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
  30. 30.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 4 (d) 5
  31. 31.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2 × 3² × 5³ (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
  32. 32.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2² × 7
  33. 33.How many factors does 78 have? (a) 6 (b) 7 (c) 9 (d) 8
  34. 34.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
  35. 35.How many factors does 84 have? (a) 12 (b) 11 (c) 10 (d) 13
  36. 36.How many factors does 65 have? (a) 2 (b) 3 (c) 5 (d) 4
  37. 37.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 8 (d) 9
  38. 38.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
  39. 39.What is the prime factorisation of 21? (a) 3 × 7² (b) 3 × 7 (c) 3³ × 7 (d) 3² × 7
  40. 40.How many factors does 96 have? (a) 12 (b) 11 (c) 13 (d) 10

Answer key

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

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