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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 3 · 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 83 have? (a) 4 (b) 2 (c) 3 (d) 1
  2. 2.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  3. 3.How many factors does 24 have? (a) 6 (b) 8 (c) 9 (d) 7
  4. 4.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2 × 5 × 7³
  5. 5.How many factors does 110 have? (a) 9 (b) 7 (c) 8 (d) 6
  6. 6.How many factors does 13 have? (a) 2 (b) 1 (c) 3 (d) 4
  7. 7.How many prime numbers are there between 30 and 50? (a) 5 (b) 4 (c) 6 (d) 7
  8. 8.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 23 (d) 1
  9. 9.How many prime numbers are there between 50 and 80? (a) 8 (b) 7 (c) 9 (d) 6
  10. 10.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 2 (d) 7
  11. 11.What is the smallest prime factor of 119? (a) 17 (b) 7 (c) 1 (d) 2
  12. 12.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3³ (c) 2 × 3² (d) 2² × 3²
  13. 13.What is the smallest prime factor of 93? (a) 31 (b) 3 (c) 2 (d) 1
  14. 14.What is the smallest prime factor of 403? (a) 31 (b) 1 (c) 13 (d) 2
  15. 15.How many factors does 94 have? (a) 5 (b) 3 (c) 2 (d) 4
  16. 16.How many prime numbers are there between 90 and 100? (a) 0 (b) 1 (c) 3 (d) 2
  17. 17.How many factors does 99 have? (a) 5 (b) 4 (c) 7 (d) 6
  18. 18.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁵ × 3² (d) 2⁴ × 3²
  19. 19.How many factors does 20 have? (a) 7 (b) 5 (c) 6 (d) 4
  20. 20.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7² (d) 2 × 3² × 7
  21. 21.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 2 (d) 1
  22. 22.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁵ × 3 (d) 2⁴ × 3
  23. 23.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2 × 3 × 5⁴
  24. 24.How many factors does 91 have? (a) 3 (b) 2 (c) 5 (d) 4
  25. 25.What is the smallest prime factor of 161? (a) 2 (b) 7 (c) 23 (d) 1
  26. 26.How many factors does 90 have? (a) 11 (b) 13 (c) 12 (d) 10
  27. 27.How many factors does 27 have? (a) 5 (b) 3 (c) 2 (d) 4
  28. 28.How many factors does 65 have? (a) 4 (b) 5 (c) 2 (d) 3
  29. 29.How many factors does 42 have? (a) 8 (b) 7 (c) 6 (d) 9
  30. 30.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5²
  31. 31.How many factors does 28 have? (a) 4 (b) 6 (c) 5 (d) 7
  32. 32.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5³ × 7 (d) 5 × 7
  33. 33.How many factors does 15 have? (a) 2 (b) 4 (c) 5 (d) 3
  34. 34.How many factors does 62 have? (a) 2 (b) 3 (c) 5 (d) 4
  35. 35.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 2 (d) 1
  36. 36.How many factors does 86 have? (a) 3 (b) 4 (c) 2 (d) 5
  37. 37.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 11 (d) 29
  38. 38.How many factors does 93 have? (a) 4 (b) 5 (c) 3 (d) 2
  39. 39.How many prime numbers are there between 90 and 110? (a) 7 (b) 6 (c) 5 (d) 4
  40. 40.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 11 (d) 2

Answer key

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

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