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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 144 · 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 93? (a) 2 (b) 3 (c) 31 (d) 1
  2. 2.How many factors does 52 have? (a) 4 (b) 5 (c) 7 (d) 6
  3. 3.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
  4. 4.What is the prime factorisation of 15? (a) 3 × 5 (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5²
  5. 5.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
  6. 6.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
  7. 7.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  8. 8.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  9. 9.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 5 (d) 6
  10. 10.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2⁴ × 3 (d) 2³ × 3
  11. 11.How many factors does 108 have? (a) 12 (b) 11 (c) 10 (d) 13
  12. 12.How many factors does 32 have? (a) 5 (b) 7 (c) 6 (d) 4
  13. 13.What is the smallest prime factor of 39? (a) 1 (b) 2 (c) 3 (d) 13
  14. 14.How many factors does 76 have? (a) 7 (b) 4 (c) 6 (d) 5
  15. 15.How many factors does 35 have? (a) 2 (b) 5 (c) 4 (d) 3
  16. 16.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2³ × 7 (d) 2⁴ × 7
  17. 17.What is the smallest prime factor of 187? (a) 2 (b) 17 (c) 1 (d) 11
  18. 18.How many factors does 62 have? (a) 4 (b) 5 (c) 2 (d) 3
  19. 19.How many prime numbers are there between 40 and 50? (a) 5 (b) 2 (c) 3 (d) 4
  20. 20.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2³ × 5 (c) 2⁴ × 5 (d) 2² × 5
  21. 21.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
  22. 22.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2² × 3² (c) 2⁴ × 3² (d) 2³ × 3²
  23. 23.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 8 (d) 9
  24. 24.How many factors does 45 have? (a) 7 (b) 5 (c) 4 (d) 6
  25. 25.How many factors does 84 have? (a) 11 (b) 10 (c) 12 (d) 13
  26. 26.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3 (d) 2 × 3²
  27. 27.What is the smallest prime factor of 51? (a) 17 (b) 1 (c) 2 (d) 3
  28. 28.How many factors does 71 have? (a) 3 (b) 2 (c) 4 (d) 1
  29. 29.How many factors does 120 have? (a) 17 (b) 14 (c) 15 (d) 16
  30. 30.How many factors does 42 have? (a) 6 (b) 8 (c) 9 (d) 7
  31. 31.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
  32. 32.How many factors does 39 have? (a) 2 (b) 5 (c) 3 (d) 4
  33. 33.How many factors does 104 have? (a) 8 (b) 6 (c) 9 (d) 7
  34. 34.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2 × 3⁴ (c) 2³ × 3 (d) 2⁴ × 3
  35. 35.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2² × 3² × 5
  36. 36.How many factors does 24 have? (a) 6 (b) 8 (c) 9 (d) 7
  37. 37.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
  38. 38.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
  39. 39.How many factors does 75 have? (a) 5 (b) 7 (c) 4 (d) 6
  40. 40.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7

Answer key

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

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