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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 95 · 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 319? (a) 29 (b) 1 (c) 2 (d) 11
  2. 2.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
  3. 3.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2 × 3² × 7
  4. 4.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 3 (d) 5
  5. 5.How many factors does 65 have? (a) 2 (b) 3 (c) 4 (d) 5
  6. 6.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2³ × 3² × 7
  7. 7.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  8. 8.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
  9. 9.How many factors does 13 have? (a) 4 (b) 2 (c) 1 (d) 3
  10. 10.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7 (c) 3 × 7² (d) 3² × 7
  11. 11.How many prime numbers are there between 70 and 80? (a) 5 (b) 4 (c) 3 (d) 2
  12. 12.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  13. 13.What is the smallest prime factor of 203? (a) 7 (b) 2 (c) 1 (d) 29
  14. 14.What is the smallest prime factor of 145? (a) 2 (b) 5 (c) 1 (d) 29
  15. 15.How many factors does 100 have? (a) 10 (b) 8 (c) 7 (d) 9
  16. 16.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 7 (d) 6
  17. 17.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5 × 7 (c) 5 × 7² (d) 5² × 7
  18. 18.What is the prime factorisation of 60? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  19. 19.What is the smallest prime factor of 39? (a) 3 (b) 13 (c) 2 (d) 1
  20. 20.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  21. 21.How many factors does 33 have? (a) 5 (b) 3 (c) 2 (d) 4
  22. 22.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  23. 23.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  24. 24.How many factors does 53 have? (a) 4 (b) 1 (c) 3 (d) 2
  25. 25.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 9 (d) 8
  26. 26.How many factors does 119 have? (a) 3 (b) 4 (c) 2 (d) 5
  27. 27.How many prime numbers are there between 70 and 90? (a) 6 (b) 4 (c) 7 (d) 5
  28. 28.How many factors does 48 have? (a) 9 (b) 11 (c) 10 (d) 8
  29. 29.How many factors does 108 have? (a) 11 (b) 10 (c) 13 (d) 12
  30. 30.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
  31. 31.What is the smallest prime factor of 51? (a) 17 (b) 2 (c) 3 (d) 1
  32. 32.How many factors does 109 have? (a) 1 (b) 2 (c) 4 (d) 3
  33. 33.How many factors does 43 have? (a) 1 (b) 2 (c) 4 (d) 3
  34. 34.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3² (c) 2 × 3² (d) 2² × 3³
  35. 35.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 2 (d) 5
  36. 36.How many factors does 115 have? (a) 5 (b) 2 (c) 4 (d) 3
  37. 37.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 11 (d) 7
  38. 38.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 4 (d) 2
  39. 39.How many factors does 92 have? (a) 4 (b) 7 (c) 5 (d) 6
  40. 40.How many factors does 62 have? (a) 5 (b) 4 (c) 2 (d) 3

Answer key

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

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