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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 169 · 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 factors does 13 have? (a) 2 (b) 1 (c) 3 (d) 4
  2. 2.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2⁴ × 3
  3. 3.How many prime numbers are there between 70 and 100? (a) 5 (b) 6 (c) 8 (d) 7
  4. 4.How many factors does 53 have? (a) 1 (b) 2 (c) 4 (d) 3
  5. 5.How many factors does 72 have? (a) 13 (b) 11 (c) 12 (d) 10
  6. 6.How many prime numbers are there between 50 and 70? (a) 4 (b) 6 (c) 3 (d) 5
  7. 7.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
  8. 8.What is the smallest prime factor of 217? (a) 31 (b) 1 (c) 7 (d) 2
  9. 9.How many factors does 30 have? (a) 9 (b) 8 (c) 6 (d) 7
  10. 10.What is the smallest prime factor of 253? (a) 23 (b) 1 (c) 2 (d) 11
  11. 11.How many factors does 120 have? (a) 17 (b) 16 (c) 15 (d) 14
  12. 12.What is the smallest prime factor of 115? (a) 1 (b) 5 (c) 2 (d) 23
  13. 13.How many factors does 102 have? (a) 8 (b) 9 (c) 7 (d) 6
  14. 14.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
  15. 15.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 4 (d) 3
  16. 16.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2⁵ × 5 × 7 (d) 2³ × 5 × 7
  17. 17.What is the smallest prime factor of 169? (a) 1 (b) 13 (c) 3 (d) 2
  18. 18.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7³
  19. 19.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 5 (d) 8
  20. 20.What is the smallest prime factor of 155? (a) 1 (b) 5 (c) 2 (d) 31
  21. 21.How many factors does 106 have? (a) 2 (b) 3 (c) 5 (d) 4
  22. 22.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 1 (d) 2
  23. 23.What is the smallest prime factor of 247? (a) 13 (b) 1 (c) 19 (d) 2
  24. 24.How many factors does 21 have? (a) 5 (b) 2 (c) 4 (d) 3
  25. 25.What is the prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2⁴ × 3²
  26. 26.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2³ × 3 × 7 (c) 2⁵ × 3 × 7 (d) 2⁴ × 3 × 7
  27. 27.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
  28. 28.What is the smallest prime factor of 377? (a) 13 (b) 1 (c) 29 (d) 2
  29. 29.How many prime numbers are there between 40 and 60? (a) 5 (b) 4 (c) 6 (d) 7
  30. 30.How many prime numbers are there between 10 and 20? (a) 4 (b) 5 (c) 6 (d) 3
  31. 31.What is the prime factorisation of 21? (a) 3 × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3² × 7
  32. 32.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁴ × 7
  33. 33.How many factors does 78 have? (a) 9 (b) 8 (c) 7 (d) 6
  34. 34.How many prime numbers are there between 30 and 60? (a) 9 (b) 8 (c) 7 (d) 6
  35. 35.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 11 (d) 2
  36. 36.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 11 (d) 5
  37. 37.What is the prime factorisation of 20? (a) 2 × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5²
  38. 38.How many factors does 98 have? (a) 4 (b) 5 (c) 6 (d) 7
  39. 39.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 2 (d) 3
  40. 40.How many factors does 41 have? (a) 3 (b) 4 (c) 1 (d) 2

Answer key

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

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