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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 16 · 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) 1 (b) 11 (c) 2 (d) 7
  2. 2.What is the smallest prime factor of 169? (a) 1 (b) 3 (c) 13 (d) 2
  3. 3.What is the smallest prime factor of 51? (a) 3 (b) 17 (c) 2 (d) 1
  4. 4.What is the smallest prime factor of 21? (a) 2 (b) 3 (c) 1 (d) 7
  5. 5.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  6. 6.How many factors does 102 have? (a) 7 (b) 8 (c) 9 (d) 6
  7. 7.How many factors does 54 have? (a) 9 (b) 7 (c) 6 (d) 8
  8. 8.How many prime numbers are there between 70 and 80? (a) 2 (b) 3 (c) 5 (d) 4
  9. 9.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2 × 3² × 7
  10. 10.How many factors does 112 have? (a) 11 (b) 10 (c) 8 (d) 9
  11. 11.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
  12. 12.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
  13. 13.How many factors does 105 have? (a) 6 (b) 9 (c) 8 (d) 7
  14. 14.How many factors does 110 have? (a) 9 (b) 8 (c) 6 (d) 7
  15. 15.How many prime numbers are there between 80 and 110? (a) 9 (b) 8 (c) 7 (d) 6
  16. 16.What is the smallest prime factor of 253? (a) 2 (b) 1 (c) 23 (d) 11
  17. 17.How many factors does 65 have? (a) 4 (b) 5 (c) 2 (d) 3
  18. 18.What is the prime factorisation of 63? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
  19. 19.How many factors does 46 have? (a) 5 (b) 3 (c) 4 (d) 2
  20. 20.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2² × 5
  21. 21.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁴ × 5 × 7
  22. 22.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
  23. 23.How many factors does 82 have? (a) 5 (b) 4 (c) 2 (d) 3
  24. 24.How many factors does 97 have? (a) 1 (b) 3 (c) 4 (d) 2
  25. 25.How many factors does 67 have? (a) 1 (b) 4 (c) 2 (d) 3
  26. 26.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2⁵ × 3 (d) 2 × 3⁴
  27. 27.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
  28. 28.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
  29. 29.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2 × 3²
  30. 30.How many factors does 20 have? (a) 6 (b) 5 (c) 4 (d) 7
  31. 31.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  32. 32.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  33. 33.What is the smallest prime factor of 57? (a) 19 (b) 2 (c) 1 (d) 3
  34. 34.How many factors does 95 have? (a) 4 (b) 2 (c) 3 (d) 5
  35. 35.How many prime numbers are there between 10 and 40? (a) 7 (b) 10 (c) 8 (d) 9
  36. 36.How many factors does 22 have? (a) 5 (b) 2 (c) 4 (d) 3
  37. 37.What is the smallest prime factor of 119? (a) 1 (b) 17 (c) 2 (d) 7
  38. 38.What is the smallest prime factor of 65? (a) 1 (b) 13 (c) 2 (d) 5
  39. 39.How many factors does 48 have? (a) 8 (b) 11 (c) 10 (d) 9
  40. 40.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2 × 3 × 5

Answer key

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

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