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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 173 · 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 10 and 40? (a) 9 (b) 7 (c) 8 (d) 10
  2. 2.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 1 (d) 5
  3. 3.How many factors does 32 have? (a) 4 (b) 6 (c) 7 (d) 5
  4. 4.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7² (c) 2 × 7 (d) 2³ × 7
  5. 5.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 7 (d) 1
  6. 6.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  7. 7.What is the smallest prime factor of 299? (a) 1 (b) 13 (c) 23 (d) 2
  8. 8.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 4 (d) 3
  9. 9.How many prime numbers are there between 90 and 120? (a) 8 (b) 5 (c) 7 (d) 6
  10. 10.How many prime numbers are there between 20 and 40? (a) 3 (b) 4 (c) 6 (d) 5
  11. 11.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  12. 12.What is the smallest prime factor of 247? (a) 2 (b) 19 (c) 13 (d) 1
  13. 13.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 8 (d) 5
  14. 14.How many prime numbers are there between 60 and 80? (a) 7 (b) 5 (c) 4 (d) 6
  15. 15.What is the smallest prime factor of 161? (a) 1 (b) 7 (c) 2 (d) 23
  16. 16.What is the smallest prime factor of 143? (a) 11 (b) 1 (c) 13 (d) 2
  17. 17.What is the prime factorisation of 56? (a) 2² × 7 (b) 2⁴ × 7 (c) 2 × 7³ (d) 2³ × 7
  18. 18.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
  19. 19.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2
  20. 20.What is the smallest prime factor of 403? (a) 2 (b) 13 (c) 31 (d) 1
  21. 21.How many factors does 51 have? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.How many factors does 31 have? (a) 2 (b) 4 (c) 3 (d) 1
  23. 23.How many factors does 42 have? (a) 9 (b) 8 (c) 7 (d) 6
  24. 24.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
  25. 25.How many factors does 29 have? (a) 3 (b) 2 (c) 1 (d) 4
  26. 26.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2 × 3 × 7³ (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  27. 27.How many factors does 88 have? (a) 7 (b) 9 (c) 8 (d) 6
  28. 28.How many prime numbers are there between 50 and 80? (a) 7 (b) 6 (c) 9 (d) 8
  29. 29.What is the smallest prime factor of 39? (a) 2 (b) 13 (c) 1 (d) 3
  30. 30.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 4 (d) 1
  31. 31.How many factors does 96 have? (a) 12 (b) 13 (c) 11 (d) 10
  32. 32.What is the smallest prime factor of 133? (a) 1 (b) 19 (c) 7 (d) 2
  33. 33.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7³ (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  34. 34.How many factors does 68 have? (a) 7 (b) 4 (c) 5 (d) 6
  35. 35.What is the smallest prime factor of 95? (a) 5 (b) 19 (c) 1 (d) 2
  36. 36.How many factors does 54 have? (a) 8 (b) 6 (c) 7 (d) 9
  37. 37.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5 (c) 2 × 5² (d) 2³ × 5
  38. 38.What is the smallest prime factor of 69? (a) 2 (b) 1 (c) 23 (d) 3
  39. 39.What is the prime factorisation of 21? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
  40. 40.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5³

Answer key

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

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