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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 114 · 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 48 have? (a) 8 (b) 9 (c) 11 (d) 10
  2. 2.How many factors does 17 have? (a) 1 (b) 3 (c) 4 (d) 2
  3. 3.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
  4. 4.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2 × 5 × 7
  5. 5.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
  6. 6.What is the smallest prime factor of 247? (a) 1 (b) 13 (c) 19 (d) 2
  7. 7.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 2 (d) 4
  8. 8.How many factors does 79 have? (a) 4 (b) 1 (c) 3 (d) 2
  9. 9.How many factors does 19 have? (a) 1 (b) 3 (c) 4 (d) 2
  10. 10.How many factors does 13 have? (a) 4 (b) 3 (c) 1 (d) 2
  11. 11.How many factors does 107 have? (a) 1 (b) 4 (c) 3 (d) 2
  12. 12.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  13. 13.How many prime numbers are there between 50 and 70? (a) 3 (b) 6 (c) 4 (d) 5
  14. 14.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 5 (d) 6
  15. 15.How many factors does 39 have? (a) 4 (b) 5 (c) 3 (d) 2
  16. 16.What is the smallest prime factor of 95? (a) 5 (b) 2 (c) 1 (d) 19
  17. 17.How many factors does 119 have? (a) 3 (b) 2 (c) 5 (d) 4
  18. 18.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  19. 19.What is the smallest prime factor of 51? (a) 2 (b) 1 (c) 3 (d) 17
  20. 20.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  21. 21.What is the smallest prime factor of 55? (a) 2 (b) 1 (c) 5 (d) 11
  22. 22.What is the smallest prime factor of 145? (a) 29 (b) 2 (c) 5 (d) 1
  23. 23.How many prime numbers are there between 60 and 70? (a) 1 (b) 4 (c) 2 (d) 3
  24. 24.How many factors does 111 have? (a) 2 (b) 3 (c) 5 (d) 4
  25. 25.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  26. 26.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
  27. 27.What is the smallest prime factor of 93? (a) 2 (b) 3 (c) 1 (d) 31
  28. 28.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 5 (d) 17
  29. 29.How many factors does 57 have? (a) 5 (b) 4 (c) 2 (d) 3
  30. 30.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
  31. 31.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2 × 3² × 5³
  32. 32.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 4 (d) 5
  33. 33.What is the smallest prime factor of 187? (a) 1 (b) 11 (c) 2 (d) 17
  34. 34.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2² × 3⁴ (d) 2⁴ × 3²
  35. 35.How many factors does 18 have? (a) 4 (b) 5 (c) 6 (d) 7
  36. 36.How many factors does 84 have? (a) 10 (b) 12 (c) 11 (d) 13
  37. 37.How many factors does 66 have? (a) 7 (b) 6 (c) 9 (d) 8
  38. 38.How many factors does 92 have? (a) 7 (b) 5 (c) 6 (d) 4
  39. 39.How many factors does 67 have? (a) 2 (b) 3 (c) 1 (d) 4
  40. 40.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁵ × 7 (c) 2 × 7⁴ (d) 2⁴ × 7

Answer key

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

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