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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 107 · 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 prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
  2. 2.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 6 (d) 7
  3. 3.What is the smallest prime factor of 55? (a) 5 (b) 2 (c) 11 (d) 1
  4. 4.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁵ × 7 (d) 2⁴ × 7
  5. 5.How many prime numbers are there between 70 and 80? (a) 3 (b) 2 (c) 4 (d) 5
  6. 6.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 1 (d) 2
  7. 7.What is the prime factorisation of 63? (a) 3 × 7² (b) 3 × 7 (c) 3³ × 7 (d) 3² × 7
  8. 8.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7 (d) 3 × 7²
  9. 9.What is the smallest prime factor of 187? (a) 11 (b) 1 (c) 2 (d) 17
  10. 10.How many factors does 39 have? (a) 2 (b) 3 (c) 5 (d) 4
  11. 11.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2³ × 3² × 7
  12. 12.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 7 (d) 1
  13. 13.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
  14. 14.What is the smallest prime factor of 161? (a) 1 (b) 7 (c) 23 (d) 2
  15. 15.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 2 (d) 1
  16. 16.How many prime numbers are there between 50 and 60? (a) 2 (b) 3 (c) 1 (d) 4
  17. 17.How many factors does 85 have? (a) 5 (b) 3 (c) 4 (d) 2
  18. 18.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 2 (d) 4
  19. 19.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2 × 3 × 5³ (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
  20. 20.How many factors does 18 have? (a) 7 (b) 4 (c) 6 (d) 5
  21. 21.How many factors does 74 have? (a) 3 (b) 2 (c) 5 (d) 4
  22. 22.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 0 (d) 1
  23. 23.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2⁵ × 3 × 7
  24. 24.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 2 (d) 1
  25. 25.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2 × 5 (d) 2³ × 5
  26. 26.How many factors does 84 have? (a) 12 (b) 10 (c) 11 (d) 13
  27. 27.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2² × 3² (c) 2⁴ × 3² (d) 2³ × 3²
  28. 28.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7
  29. 29.How many factors does 15 have? (a) 3 (b) 5 (c) 2 (d) 4
  30. 30.What is the smallest prime factor of 49? (a) 3 (b) 1 (c) 7 (d) 2
  31. 31.How many factors does 100 have? (a) 8 (b) 7 (c) 9 (d) 10
  32. 32.How many factors does 28 have? (a) 6 (b) 5 (c) 7 (d) 4
  33. 33.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
  34. 34.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2³ × 5 (d) 2² × 5
  35. 35.What is the smallest prime factor of 121? (a) 1 (b) 11 (c) 3 (d) 2
  36. 36.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3³
  37. 37.How many prime numbers are there between 90 and 110? (a) 6 (b) 4 (c) 7 (d) 5
  38. 38.What is the smallest prime factor of 39? (a) 2 (b) 13 (c) 3 (d) 1
  39. 39.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 7 (d) 9
  40. 40.How many factors does 105 have? (a) 8 (b) 7 (c) 6 (d) 9

Answer key

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

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