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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 61 · 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 80 and 100? (a) 5 (b) 4 (c) 2 (d) 3
  2. 2.How many prime numbers are there between 10 and 40? (a) 7 (b) 10 (c) 9 (d) 8
  3. 3.How many factors does 93 have? (a) 4 (b) 5 (c) 3 (d) 2
  4. 4.What is the smallest prime factor of 145? (a) 2 (b) 1 (c) 5 (d) 29
  5. 5.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 5 (d) 1
  6. 6.What is the smallest prime factor of 299? (a) 23 (b) 1 (c) 2 (d) 13
  7. 7.How many factors does 82 have? (a) 2 (b) 4 (c) 3 (d) 5
  8. 8.How many factors does 105 have? (a) 6 (b) 9 (c) 8 (d) 7
  9. 9.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 13 (d) 7
  10. 10.How many factors does 80 have? (a) 9 (b) 11 (c) 8 (d) 10
  11. 11.How many factors does 89 have? (a) 1 (b) 3 (c) 2 (d) 4
  12. 12.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 6 (d) 8
  13. 13.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 5 (d) 6
  14. 14.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 8 (d) 7
  15. 15.What is the smallest prime factor of 35? (a) 5 (b) 2 (c) 1 (d) 7
  16. 16.What is the prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2 × 5² (d) 2³ × 5
  17. 17.How many prime numbers are there between 10 and 20? (a) 5 (b) 6 (c) 3 (d) 4
  18. 18.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3² × 5 (c) 3 × 5 (d) 3 × 5²
  19. 19.What is the smallest prime factor of 49? (a) 7 (b) 3 (c) 2 (d) 1
  20. 20.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2 × 3 × 5³ (c) 2² × 3 × 5 (d) 2⁴ × 3 × 5
  21. 21.How many factors does 75 have? (a) 7 (b) 6 (c) 4 (d) 5
  22. 22.How many factors does 43 have? (a) 3 (b) 2 (c) 4 (d) 1
  23. 23.How many prime numbers are there between 50 and 60? (a) 2 (b) 3 (c) 4 (d) 1
  24. 24.How many factors does 78 have? (a) 9 (b) 7 (c) 8 (d) 6
  25. 25.How many factors does 108 have? (a) 13 (b) 11 (c) 10 (d) 12
  26. 26.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 4 (d) 6
  27. 27.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 2 (d) 11
  28. 28.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 5 (d) 4
  29. 29.How many prime numbers are there between 80 and 110? (a) 8 (b) 6 (c) 9 (d) 7
  30. 30.How many prime numbers are there between 80 and 90? (a) 3 (b) 4 (c) 2 (d) 1
  31. 31.What is the prime factorisation of 14? (a) 2 × 7² (b) 2 × 7 (c) 2² × 7 (d) 2³ × 7
  32. 32.How many factors does 44 have? (a) 5 (b) 4 (c) 6 (d) 7
  33. 33.What is the prime factorisation of 45? (a) 3 × 5 (b) 3 × 5² (c) 3² × 5 (d) 3³ × 5
  34. 34.What is the smallest prime factor of 203? (a) 2 (b) 29 (c) 1 (d) 7
  35. 35.How many factors does 88 have? (a) 7 (b) 8 (c) 6 (d) 9
  36. 36.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7 (c) 5 × 7² (d) 5³ × 7
  37. 37.What is the smallest prime factor of 85? (a) 5 (b) 1 (c) 17 (d) 2
  38. 38.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  39. 39.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁵ × 3 × 7 (d) 2⁴ × 3 × 7
  40. 40.How many factors does 65 have? (a) 4 (b) 5 (c) 2 (d) 3

Answer key

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

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