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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 53 · 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) 5 (b) 6 (c) 7 (d) 4
  2. 2.How many factors does 30 have? (a) 7 (b) 8 (c) 9 (d) 6
  3. 3.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2² × 3 × 7
  4. 4.What is the smallest prime factor of 55? (a) 2 (b) 5 (c) 11 (d) 1
  5. 5.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 2 (d) 1
  6. 6.How many factors does 90 have? (a) 11 (b) 12 (c) 13 (d) 10
  7. 7.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2² × 5 (d) 2³ × 5
  8. 8.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
  9. 9.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7⁴
  10. 10.What is the smallest prime factor of 119? (a) 2 (b) 7 (c) 17 (d) 1
  11. 11.How many factors does 102 have? (a) 8 (b) 9 (c) 7 (d) 6
  12. 12.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  13. 13.How many factors does 37 have? (a) 4 (b) 1 (c) 2 (d) 3
  14. 14.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 3 (d) 6
  15. 15.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 5 (d) 13
  16. 16.How many prime numbers are there between 30 and 60? (a) 6 (b) 9 (c) 7 (d) 8
  17. 17.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 8 (d) 6
  18. 18.What is the smallest prime factor of 247? (a) 2 (b) 19 (c) 1 (d) 13
  19. 19.What is the prime factorisation of 63? (a) 3 × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3² × 7
  20. 20.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  21. 21.What is the smallest prime factor of 145? (a) 29 (b) 5 (c) 1 (d) 2
  22. 22.How many factors does 79 have? (a) 1 (b) 4 (c) 3 (d) 2
  23. 23.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 5 (d) 4
  24. 24.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 11 (d) 2
  25. 25.How many factors does 88 have? (a) 6 (b) 8 (c) 7 (d) 9
  26. 26.How many factors does 67 have? (a) 4 (b) 2 (c) 3 (d) 1
  27. 27.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 3 (d) 4
  28. 28.How many factors does 56 have? (a) 9 (b) 6 (c) 7 (d) 8
  29. 29.What is the smallest prime factor of 203? (a) 29 (b) 7 (c) 2 (d) 1
  30. 30.How many factors does 101 have? (a) 3 (b) 2 (c) 1 (d) 4
  31. 31.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 17 (d) 2
  32. 32.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 5 (d) 3
  33. 33.How many factors does 66 have? (a) 8 (b) 9 (c) 7 (d) 6
  34. 34.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 9 (d) 7
  35. 35.How many factors does 95 have? (a) 5 (b) 2 (c) 3 (d) 4
  36. 36.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3² × 5 × 7 (c) 3³ × 5 × 7 (d) 3 × 5 × 7²
  37. 37.How many prime numbers are there between 40 and 60? (a) 6 (b) 4 (c) 5 (d) 7
  38. 38.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
  39. 39.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 7 (d) 1
  40. 40.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 5 (d) 6

Answer key

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

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