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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 179 · 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.What is the smallest prime factor of 187? (a) 1 (b) 2 (c) 17 (d) 11
  2. 2.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2² × 3 × 5
  3. 3.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 17 (d) 2
  4. 4.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 3 (d) 11
  5. 5.How many factors does 91 have? (a) 4 (b) 2 (c) 5 (d) 3
  6. 6.How many factors does 30 have? (a) 9 (b) 6 (c) 8 (d) 7
  7. 7.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2³ × 3² × 7
  8. 8.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2 × 3⁴ (c) 2⁵ × 3 (d) 2³ × 3
  9. 9.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
  10. 10.How many factors does 100 have? (a) 8 (b) 9 (c) 10 (d) 7
  11. 11.How many factors does 36 have? (a) 7 (b) 10 (c) 8 (d) 9
  12. 12.How many factors does 33 have? (a) 4 (b) 5 (c) 2 (d) 3
  13. 13.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 5 (d) 1
  14. 14.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 3 (d) 4
  15. 15.How many prime numbers are there between 20 and 50? (a) 7 (b) 8 (c) 6 (d) 9
  16. 16.What is the smallest prime factor of 341? (a) 1 (b) 31 (c) 11 (d) 2
  17. 17.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2⁵ × 7
  18. 18.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 3 (d) 29
  19. 19.How many factors does 26 have? (a) 4 (b) 2 (c) 5 (d) 3
  20. 20.How many prime numbers are there between 70 and 80? (a) 3 (b) 5 (c) 2 (d) 4
  21. 21.What is the smallest prime factor of 217? (a) 7 (b) 31 (c) 2 (d) 1
  22. 22.How many factors does 32 have? (a) 5 (b) 7 (c) 4 (d) 6
  23. 23.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 23 (d) 7
  24. 24.What is the smallest prime factor of 209? (a) 2 (b) 11 (c) 1 (d) 19
  25. 25.What is the smallest prime factor of 49? (a) 2 (b) 1 (c) 7 (d) 3
  26. 26.What is the smallest prime factor of 253? (a) 1 (b) 23 (c) 2 (d) 11
  27. 27.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  28. 28.How many factors does 97 have? (a) 1 (b) 4 (c) 3 (d) 2
  29. 29.How many prime numbers are there between 90 and 120? (a) 5 (b) 7 (c) 6 (d) 8
  30. 30.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2² × 5 (d) 2³ × 5
  31. 31.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 4 (d) 2
  32. 32.How many factors does 52 have? (a) 7 (b) 6 (c) 5 (d) 4
  33. 33.How many factors does 39 have? (a) 5 (b) 4 (c) 3 (d) 2
  34. 34.What is the prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  35. 35.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 1 (d) 2
  36. 36.How many factors does 61 have? (a) 1 (b) 4 (c) 3 (d) 2
  37. 37.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  38. 38.How many prime numbers are there between 90 and 100? (a) 3 (b) 2 (c) 0 (d) 1
  39. 39.How many factors does 15 have? (a) 3 (b) 4 (c) 2 (d) 5
  40. 40.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2

Answer key

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

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