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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 7 · 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.How many prime numbers are there between 40 and 50? (a) 2 (b) 5 (c) 3 (d) 4
  2. 2.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
  3. 3.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2 × 3 × 7³ (d) 2² × 3 × 7
  4. 4.How many factors does 66 have? (a) 6 (b) 8 (c) 7 (d) 9
  5. 5.What is the smallest prime factor of 169? (a) 3 (b) 1 (c) 2 (d) 13
  6. 6.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
  7. 7.How many factors does 89 have? (a) 3 (b) 2 (c) 4 (d) 1
  8. 8.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 2 (d) 13
  9. 9.What is the smallest prime factor of 209? (a) 2 (b) 19 (c) 11 (d) 1
  10. 10.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 4 (d) 3
  11. 11.What is the smallest prime factor of 299? (a) 1 (b) 13 (c) 23 (d) 2
  12. 12.How many prime numbers are there between 70 and 90? (a) 5 (b) 4 (c) 7 (d) 6
  13. 13.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2² × 7 (c) 2 × 7³ (d) 2³ × 7
  14. 14.How many factors does 41 have? (a) 3 (b) 4 (c) 1 (d) 2
  15. 15.How many factors does 60 have? (a) 11 (b) 13 (c) 10 (d) 12
  16. 16.What is the smallest prime factor of 221? (a) 1 (b) 13 (c) 17 (d) 2
  17. 17.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 2 (d) 3
  18. 18.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5³
  19. 19.How many factors does 65 have? (a) 5 (b) 2 (c) 3 (d) 4
  20. 20.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5 (d) 3 × 5²
  21. 21.How many factors does 58 have? (a) 5 (b) 3 (c) 2 (d) 4
  22. 22.How many factors does 48 have? (a) 9 (b) 8 (c) 11 (d) 10
  23. 23.How many factors does 51 have? (a) 2 (b) 4 (c) 3 (d) 5
  24. 24.What is the smallest prime factor of 403? (a) 31 (b) 1 (c) 13 (d) 2
  25. 25.How many factors does 22 have? (a) 2 (b) 5 (c) 4 (d) 3
  26. 26.How many factors does 114 have? (a) 7 (b) 6 (c) 9 (d) 8
  27. 27.How many factors does 29 have? (a) 1 (b) 4 (c) 3 (d) 2
  28. 28.How many factors does 47 have? (a) 4 (b) 3 (c) 1 (d) 2
  29. 29.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2² × 3⁴ (c) 2⁴ × 3² (d) 2³ × 3²
  30. 30.How many factors does 69 have? (a) 4 (b) 2 (c) 5 (d) 3
  31. 31.What is the smallest prime factor of 341? (a) 1 (b) 2 (c) 11 (d) 31
  32. 32.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2 × 3² (c) 2² × 3 (d) 2 × 3
  33. 33.What is the smallest prime factor of 253? (a) 1 (b) 11 (c) 2 (d) 23
  34. 34.What is the smallest prime factor of 319? (a) 11 (b) 2 (c) 1 (d) 29
  35. 35.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 5 (d) 4
  36. 36.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2³ × 3² × 7
  37. 37.How many factors does 28 have? (a) 4 (b) 5 (c) 7 (d) 6
  38. 38.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 7 (d) 2
  39. 39.How many factors does 62 have? (a) 3 (b) 4 (c) 5 (d) 2
  40. 40.What is the smallest prime factor of 95? (a) 2 (b) 19 (c) 5 (d) 1

Answer key

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

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