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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 200 · 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 88 have? (a) 7 (b) 9 (c) 6 (d) 8
  2. 2.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  3. 3.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 29 (d) 11
  4. 4.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 7 (d) 1
  5. 5.What is the smallest prime factor of 161? (a) 23 (b) 7 (c) 2 (d) 1
  6. 6.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
  7. 7.What is the smallest prime factor of 221? (a) 2 (b) 13 (c) 17 (d) 1
  8. 8.What is the smallest prime factor of 51? (a) 17 (b) 3 (c) 2 (d) 1
  9. 9.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 6 (d) 9
  10. 10.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
  11. 11.What is the prime factorisation of 28? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  12. 12.What is the smallest prime factor of 377? (a) 13 (b) 2 (c) 29 (d) 1
  13. 13.What is the smallest prime factor of 21? (a) 3 (b) 1 (c) 2 (d) 7
  14. 14.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2⁵ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁴ × 5 × 7
  15. 15.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 11 (d) 1
  16. 16.How many prime numbers are there between 30 and 50? (a) 7 (b) 4 (c) 6 (d) 5
  17. 17.What is the prime factorisation of 45? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
  18. 18.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 4 (d) 3
  19. 19.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  20. 20.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 3 (d) 29
  21. 21.How many factors does 19 have? (a) 1 (b) 2 (c) 4 (d) 3
  22. 22.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2⁵ × 7
  23. 23.How many factors does 40 have? (a) 8 (b) 6 (c) 7 (d) 9
  24. 24.How many factors does 15 have? (a) 2 (b) 3 (c) 5 (d) 4
  25. 25.What is the smallest prime factor of 39? (a) 13 (b) 2 (c) 1 (d) 3
  26. 26.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2⁴ × 7 (c) 2² × 7 (d) 2³ × 7
  27. 27.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 9 (d) 7
  28. 28.How many factors does 24 have? (a) 9 (b) 7 (c) 8 (d) 6
  29. 29.How many factors does 55 have? (a) 4 (b) 5 (c) 2 (d) 3
  30. 30.What is the smallest prime factor of 35? (a) 2 (b) 5 (c) 7 (d) 1
  31. 31.How many factors does 38 have? (a) 5 (b) 4 (c) 3 (d) 2
  32. 32.What is the prime factorisation of 21? (a) 3 × 7² (b) 3 × 7 (c) 3³ × 7 (d) 3² × 7
  33. 33.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 7 (d) 6
  34. 34.How many factors does 89 have? (a) 2 (b) 4 (c) 3 (d) 1
  35. 35.How many factors does 119 have? (a) 2 (b) 5 (c) 3 (d) 4
  36. 36.How many factors does 73 have? (a) 4 (b) 3 (c) 2 (d) 1
  37. 37.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 4 (d) 5
  38. 38.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  39. 39.What is the smallest prime factor of 121? (a) 2 (b) 11 (c) 3 (d) 1
  40. 40.What is the smallest prime factor of 341? (a) 1 (b) 31 (c) 2 (d) 11

Answer key

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

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