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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 18 · 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 126? (a) 2 × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  2. 2.How many prime numbers are there between 40 and 70? (a) 6 (b) 9 (c) 8 (d) 7
  3. 3.How many factors does 102 have? (a) 6 (b) 7 (c) 8 (d) 9
  4. 4.How many factors does 25 have? (a) 2 (b) 3 (c) 1 (d) 4
  5. 5.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 1 (d) 13
  6. 6.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 2 (d) 13
  7. 7.How many factors does 55 have? (a) 4 (b) 3 (c) 5 (d) 2
  8. 8.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3² (c) 2³ × 3² (d) 2² × 3³
  9. 9.How many prime numbers are there between 90 and 110? (a) 7 (b) 4 (c) 5 (d) 6
  10. 10.How many factors does 115 have? (a) 4 (b) 5 (c) 3 (d) 2
  11. 11.What is the smallest prime factor of 377? (a) 2 (b) 13 (c) 29 (d) 1
  12. 12.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
  13. 13.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 2 (d) 3
  14. 14.How many factors does 56 have? (a) 7 (b) 9 (c) 8 (d) 6
  15. 15.How many prime numbers are there between 40 and 50? (a) 5 (b) 2 (c) 3 (d) 4
  16. 16.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
  17. 17.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3² (c) 2² × 3² (d) 2 × 3³
  18. 18.How many factors does 35 have? (a) 2 (b) 3 (c) 5 (d) 4
  19. 19.What is the prime factorisation of 360? (a) 2³ × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2² × 3² × 5
  20. 20.What is the smallest prime factor of 51? (a) 17 (b) 1 (c) 3 (d) 2
  21. 21.How many prime numbers are there between 50 and 80? (a) 7 (b) 9 (c) 8 (d) 6
  22. 22.How many factors does 41 have? (a) 1 (b) 3 (c) 2 (d) 4
  23. 23.How many factors does 52 have? (a) 7 (b) 4 (c) 5 (d) 6
  24. 24.What is the smallest prime factor of 319? (a) 1 (b) 11 (c) 2 (d) 29
  25. 25.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
  26. 26.What is the smallest prime factor of 39? (a) 3 (b) 13 (c) 2 (d) 1
  27. 27.How many factors does 36 have? (a) 8 (b) 7 (c) 10 (d) 9
  28. 28.What is the smallest prime factor of 87? (a) 2 (b) 29 (c) 3 (d) 1
  29. 29.How many factors does 40 have? (a) 9 (b) 6 (c) 7 (d) 8
  30. 30.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
  31. 31.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 4 (d) 6
  32. 32.How many factors does 59 have? (a) 2 (b) 3 (c) 4 (d) 1
  33. 33.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 1 (d) 3
  34. 34.How many factors does 119 have? (a) 5 (b) 2 (c) 3 (d) 4
  35. 35.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  36. 36.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 4 (d) 5
  37. 37.What is the smallest prime factor of 115? (a) 1 (b) 23 (c) 5 (d) 2
  38. 38.How many factors does 83 have? (a) 4 (b) 1 (c) 2 (d) 3
  39. 39.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 1 (d) 3
  40. 40.How many factors does 76 have? (a) 7 (b) 6 (c) 4 (d) 5

Answer key

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

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