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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 163 · 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 77? (a) 2 (b) 7 (c) 1 (d) 11
  2. 2.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
  3. 3.What is the smallest prime factor of 377? (a) 1 (b) 29 (c) 13 (d) 2
  4. 4.How many factors does 88 have? (a) 9 (b) 7 (c) 6 (d) 8
  5. 5.How many prime numbers are there between 60 and 80? (a) 5 (b) 6 (c) 7 (d) 4
  6. 6.How many factors does 79 have? (a) 1 (b) 2 (c) 4 (d) 3
  7. 7.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2³ × 5
  8. 8.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 5 (d) 6
  9. 9.How many prime numbers are there between 10 and 20? (a) 5 (b) 4 (c) 6 (d) 3
  10. 10.What is the smallest prime factor of 217? (a) 1 (b) 31 (c) 2 (d) 7
  11. 11.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
  12. 12.How many factors does 85 have? (a) 5 (b) 2 (c) 3 (d) 4
  13. 13.How many factors does 49 have? (a) 3 (b) 4 (c) 2 (d) 1
  14. 14.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 23 (d) 1
  15. 15.How many factors does 111 have? (a) 5 (b) 4 (c) 2 (d) 3
  16. 16.What is the smallest prime factor of 115? (a) 2 (b) 5 (c) 1 (d) 23
  17. 17.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
  18. 18.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2⁴ × 5 × 7 (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  19. 19.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 1 (d) 2
  20. 20.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2 × 3 (c) 2² × 3 (d) 2 × 3²
  21. 21.How many prime numbers are there between 50 and 80? (a) 8 (b) 7 (c) 6 (d) 9
  22. 22.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 2 (d) 13
  23. 23.How many factors does 37 have? (a) 4 (b) 1 (c) 2 (d) 3
  24. 24.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 5 (d) 7
  25. 25.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
  26. 26.How many factors does 46 have? (a) 5 (b) 2 (c) 3 (d) 4
  27. 27.How many factors does 44 have? (a) 6 (b) 5 (c) 4 (d) 7
  28. 28.How many factors does 70 have? (a) 7 (b) 8 (c) 9 (d) 6
  29. 29.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2³ × 3²
  30. 30.How many factors does 103 have? (a) 2 (b) 4 (c) 3 (d) 1
  31. 31.How many prime numbers are there between 50 and 70? (a) 4 (b) 5 (c) 6 (d) 3
  32. 32.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 3 (d) 5
  33. 33.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5³
  34. 34.What is the smallest prime factor of 155? (a) 5 (b) 31 (c) 1 (d) 2
  35. 35.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁵ × 3² (c) 2³ × 3² (d) 2⁴ × 3²
  36. 36.What is the prime factorisation of 420? (a) 2³ × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2 × 3 × 5 × 7
  37. 37.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3 × 7
  38. 38.What is the smallest prime factor of 169? (a) 1 (b) 3 (c) 2 (d) 13
  39. 39.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2² × 3
  40. 40.How many factors does 96 have? (a) 10 (b) 13 (c) 12 (d) 11

Answer key

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

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