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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 63 · 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 94 have? (a) 3 (b) 5 (c) 4 (d) 2
  2. 2.What is the smallest prime factor of 115? (a) 1 (b) 23 (c) 2 (d) 5
  3. 3.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
  4. 4.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 4 (d) 5
  5. 5.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
  6. 6.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 5 (d) 4
  7. 7.What is the prime factorisation of 14? (a) 2² × 7 (b) 2 × 7 (c) 2 × 7² (d) 2³ × 7
  8. 8.How many factors does 61 have? (a) 1 (b) 3 (c) 4 (d) 2
  9. 9.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  10. 10.How many factors does 17 have? (a) 1 (b) 4 (c) 3 (d) 2
  11. 11.How many factors does 103 have? (a) 1 (b) 4 (c) 3 (d) 2
  12. 12.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 6 (d) 5
  13. 13.How many factors does 81 have? (a) 4 (b) 5 (c) 3 (d) 6
  14. 14.How many factors does 74 have? (a) 3 (b) 5 (c) 4 (d) 2
  15. 15.What is the smallest prime factor of 69? (a) 1 (b) 3 (c) 2 (d) 23
  16. 16.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2⁵ × 5
  17. 17.What is the smallest prime factor of 155? (a) 2 (b) 31 (c) 5 (d) 1
  18. 18.How many factors does 106 have? (a) 5 (b) 3 (c) 2 (d) 4
  19. 19.What is the smallest prime factor of 247? (a) 1 (b) 19 (c) 13 (d) 2
  20. 20.How many factors does 27 have? (a) 3 (b) 5 (c) 2 (d) 4
  21. 21.How many factors does 34 have? (a) 4 (b) 2 (c) 3 (d) 5
  22. 22.How many factors does 83 have? (a) 4 (b) 1 (c) 3 (d) 2
  23. 23.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3 × 5 × 7²
  24. 24.How many factors does 111 have? (a) 5 (b) 2 (c) 4 (d) 3
  25. 25.How many prime numbers are there between 90 and 110? (a) 4 (b) 7 (c) 5 (d) 6
  26. 26.How many factors does 12 have? (a) 7 (b) 4 (c) 6 (d) 5
  27. 27.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 7 (d) 13
  28. 28.What is the smallest prime factor of 319? (a) 11 (b) 1 (c) 29 (d) 2
  29. 29.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2³ × 5 (d) 2² × 5
  30. 30.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3² (c) 2 × 3³ (d) 2² × 3
  31. 31.What is the smallest prime factor of 377? (a) 1 (b) 29 (c) 13 (d) 2
  32. 32.How many factors does 45 have? (a) 7 (b) 4 (c) 5 (d) 6
  33. 33.How many prime numbers are there between 70 and 90? (a) 7 (b) 4 (c) 6 (d) 5
  34. 34.How many factors does 49 have? (a) 2 (b) 1 (c) 4 (d) 3
  35. 35.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
  36. 36.How many factors does 41 have? (a) 4 (b) 1 (c) 3 (d) 2
  37. 37.How many factors does 108 have? (a) 11 (b) 13 (c) 12 (d) 10
  38. 38.How many factors does 15 have? (a) 2 (b) 3 (c) 4 (d) 5
  39. 39.How many factors does 38 have? (a) 5 (b) 3 (c) 2 (d) 4
  40. 40.How many factors does 66 have? (a) 6 (b) 7 (c) 8 (d) 9

Answer key

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

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