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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 121 · 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 25 have? (a) 2 (b) 3 (c) 1 (d) 4
  2. 2.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 29 (d) 3
  3. 3.What is the smallest prime factor of 203? (a) 7 (b) 1 (c) 29 (d) 2
  4. 4.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2² × 3 × 7
  5. 5.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  6. 6.How many factors does 14 have? (a) 5 (b) 4 (c) 2 (d) 3
  7. 7.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 6 (d) 4
  8. 8.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 1 (d) 2
  9. 9.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2³ × 3
  10. 10.How many prime numbers are there between 80 and 100? (a) 5 (b) 3 (c) 4 (d) 2
  11. 11.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 7 (d) 23
  12. 12.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 6 (d) 7
  13. 13.How many factors does 117 have? (a) 4 (b) 5 (c) 6 (d) 7
  14. 14.How many prime numbers are there between 20 and 50? (a) 7 (b) 6 (c) 8 (d) 9
  15. 15.How many factors does 77 have? (a) 3 (b) 4 (c) 2 (d) 5
  16. 16.How many factors does 60 have? (a) 13 (b) 11 (c) 10 (d) 12
  17. 17.How many factors does 45 have? (a) 6 (b) 4 (c) 7 (d) 5
  18. 18.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  19. 19.What is the smallest prime factor of 121? (a) 11 (b) 3 (c) 2 (d) 1
  20. 20.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2⁴ × 3²
  21. 21.How many prime numbers are there between 10 and 40? (a) 7 (b) 10 (c) 9 (d) 8
  22. 22.How many factors does 89 have? (a) 3 (b) 2 (c) 1 (d) 4
  23. 23.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 2 (d) 11
  24. 24.How many factors does 100 have? (a) 9 (b) 10 (c) 7 (d) 8
  25. 25.How many factors does 42 have? (a) 9 (b) 6 (c) 8 (d) 7
  26. 26.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 5 (d) 7
  27. 27.How many factors does 101 have? (a) 2 (b) 3 (c) 1 (d) 4
  28. 28.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁵ × 3 × 5 (d) 2⁴ × 3 × 5
  29. 29.What is the smallest prime factor of 33? (a) 2 (b) 3 (c) 11 (d) 1
  30. 30.What is the smallest prime factor of 217? (a) 7 (b) 1 (c) 31 (d) 2
  31. 31.How many factors does 54 have? (a) 8 (b) 9 (c) 6 (d) 7
  32. 32.How many prime numbers are there between 70 and 90? (a) 7 (b) 6 (c) 5 (d) 4
  33. 33.How many factors does 30 have? (a) 6 (b) 9 (c) 7 (d) 8
  34. 34.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  35. 35.How many prime numbers are there between 50 and 80? (a) 7 (b) 8 (c) 9 (d) 6
  36. 36.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁵ × 5 × 7
  37. 37.What is the prime factorisation of 63? (a) 3² × 7 (b) 3 × 7 (c) 3 × 7² (d) 3³ × 7
  38. 38.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁵ × 5 (d) 2⁴ × 5
  39. 39.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 4 (d) 1
  40. 40.What is the smallest prime factor of 209? (a) 1 (b) 2 (c) 11 (d) 19

Answer key

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

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