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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 210 · 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 50? (a) 7 (b) 4 (c) 5 (d) 6
  2. 2.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
  3. 3.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  4. 4.What is the smallest prime factor of 161? (a) 1 (b) 2 (c) 7 (d) 23
  5. 5.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  6. 6.What is the smallest prime factor of 145? (a) 5 (b) 2 (c) 1 (d) 29
  7. 7.How many factors does 63 have? (a) 6 (b) 4 (c) 5 (d) 7
  8. 8.What is the smallest prime factor of 119? (a) 17 (b) 1 (c) 2 (d) 7
  9. 9.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5 (c) 2 × 5² (d) 2² × 5
  10. 10.How many factors does 14 have? (a) 2 (b) 3 (c) 5 (d) 4
  11. 11.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 5 (d) 8
  12. 12.How many prime numbers are there between 80 and 110? (a) 8 (b) 6 (c) 7 (d) 9
  13. 13.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 2 (d) 1
  14. 14.How many prime numbers are there between 10 and 40? (a) 8 (b) 9 (c) 7 (d) 10
  15. 15.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7 (c) 2² × 7 (d) 2 × 7²
  16. 16.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7³ (d) 2⁴ × 7
  17. 17.What is the smallest prime factor of 85? (a) 2 (b) 5 (c) 1 (d) 17
  18. 18.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5 × 7
  19. 19.How many prime numbers are there between 40 and 60? (a) 6 (b) 5 (c) 4 (d) 7
  20. 20.What is the prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  21. 21.How many factors does 75 have? (a) 4 (b) 7 (c) 5 (d) 6
  22. 22.How many factors does 34 have? (a) 3 (b) 4 (c) 2 (d) 5
  23. 23.How many factors does 88 have? (a) 9 (b) 6 (c) 7 (d) 8
  24. 24.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 6 (d) 5
  25. 25.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
  26. 26.How many prime numbers are there between 90 and 120? (a) 7 (b) 8 (c) 6 (d) 5
  27. 27.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2⁴ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2³ × 5 × 7
  28. 28.What is the prime factorisation of 36? (a) 2² × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2 × 3²
  29. 29.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 2 (d) 11
  30. 30.How many factors does 97 have? (a) 3 (b) 1 (c) 2 (d) 4
  31. 31.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  32. 32.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
  33. 33.How many factors does 45 have? (a) 6 (b) 4 (c) 7 (d) 5
  34. 34.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  35. 35.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 2 (d) 11
  36. 36.What is the smallest prime factor of 35? (a) 7 (b) 5 (c) 1 (d) 2
  37. 37.How many factors does 51 have? (a) 2 (b) 4 (c) 3 (d) 5
  38. 38.What is the smallest prime factor of 247? (a) 13 (b) 2 (c) 19 (d) 1
  39. 39.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 5 (d) 2
  40. 40.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 4 (d) 5

Answer key

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

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