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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 27 · 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 79 have? (a) 2 (b) 4 (c) 3 (d) 1
  2. 2.What is the smallest prime factor of 95? (a) 19 (b) 5 (c) 1 (d) 2
  3. 3.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
  4. 4.What is the smallest prime factor of 49? (a) 3 (b) 2 (c) 1 (d) 7
  5. 5.What is the smallest prime factor of 247? (a) 13 (b) 2 (c) 1 (d) 19
  6. 6.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 3 (d) 2
  7. 7.How many prime numbers are there between 60 and 70? (a) 2 (b) 4 (c) 1 (d) 3
  8. 8.How many factors does 93 have? (a) 5 (b) 4 (c) 2 (d) 3
  9. 9.How many factors does 40 have? (a) 6 (b) 7 (c) 9 (d) 8
  10. 10.How many factors does 112 have? (a) 8 (b) 10 (c) 11 (d) 9
  11. 11.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  12. 12.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 7 (d) 6
  13. 13.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 31 (d) 1
  14. 14.How many factors does 120 have? (a) 17 (b) 14 (c) 15 (d) 16
  15. 15.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 4 (d) 3
  16. 16.How many factors does 77 have? (a) 2 (b) 5 (c) 3 (d) 4
  17. 17.How many factors does 13 have? (a) 4 (b) 2 (c) 1 (d) 3
  18. 18.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 3 (d) 5
  19. 19.How many factors does 76 have? (a) 4 (b) 6 (c) 5 (d) 7
  20. 20.How many factors does 36 have? (a) 9 (b) 8 (c) 10 (d) 7
  21. 21.How many factors does 63 have? (a) 7 (b) 4 (c) 6 (d) 5
  22. 22.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 3 (d) 1
  23. 23.How many prime numbers are there between 50 and 80? (a) 6 (b) 9 (c) 7 (d) 8
  24. 24.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
  25. 25.How many factors does 92 have? (a) 6 (b) 5 (c) 4 (d) 7
  26. 26.What is the prime factorisation of 45? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
  27. 27.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 5 (d) 7
  28. 28.How many factors does 97 have? (a) 2 (b) 4 (c) 1 (d) 3
  29. 29.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 1 (d) 11
  30. 30.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 1 (d) 4
  31. 31.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  32. 32.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2³ × 7 (d) 2⁴ × 7
  33. 33.How many factors does 105 have? (a) 8 (b) 6 (c) 7 (d) 9
  34. 34.How many factors does 24 have? (a) 9 (b) 6 (c) 8 (d) 7
  35. 35.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
  36. 36.What is the prime factorisation of 35? (a) 5 × 7 (b) 5² × 7 (c) 5 × 7² (d) 5³ × 7
  37. 37.What is the smallest prime factor of 33? (a) 1 (b) 3 (c) 11 (d) 2
  38. 38.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2⁵ × 5 × 7 (d) 2⁴ × 5 × 7
  39. 39.How many factors does 66 have? (a) 7 (b) 9 (c) 6 (d) 8
  40. 40.What is the smallest prime factor of 341? (a) 11 (b) 31 (c) 1 (d) 2

Answer key

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

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