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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 45 · 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 63 have? (a) 4 (b) 6 (c) 5 (d) 7
  2. 2.How many factors does 76 have? (a) 7 (b) 5 (c) 4 (d) 6
  3. 3.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
  4. 4.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 4 (d) 2
  5. 5.What is the prime factorisation of 360? (a) 2³ × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2 × 3² × 5³ (d) 2² × 3² × 5
  6. 6.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2³ × 3²
  7. 7.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
  8. 8.What is the smallest prime factor of 51? (a) 2 (b) 1 (c) 17 (d) 3
  9. 9.What is the smallest prime factor of 77? (a) 7 (b) 11 (c) 1 (d) 2
  10. 10.What is the smallest prime factor of 217? (a) 31 (b) 7 (c) 2 (d) 1
  11. 11.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2² × 3
  12. 12.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2³ × 3
  13. 13.How many factors does 42 have? (a) 7 (b) 6 (c) 8 (d) 9
  14. 14.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
  15. 15.How many factors does 95 have? (a) 2 (b) 5 (c) 4 (d) 3
  16. 16.How many prime numbers are there between 60 and 80? (a) 5 (b) 6 (c) 4 (d) 7
  17. 17.How many prime numbers are there between 20 and 40? (a) 3 (b) 5 (c) 4 (d) 6
  18. 18.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7⁴
  19. 19.How many factors does 52 have? (a) 6 (b) 5 (c) 4 (d) 7
  20. 20.How many factors does 77 have? (a) 4 (b) 2 (c) 3 (d) 5
  21. 21.What is the smallest prime factor of 145? (a) 2 (b) 5 (c) 1 (d) 29
  22. 22.How many factors does 50 have? (a) 6 (b) 5 (c) 7 (d) 4
  23. 23.How many factors does 106 have? (a) 2 (b) 3 (c) 5 (d) 4
  24. 24.How many factors does 70 have? (a) 9 (b) 8 (c) 7 (d) 6
  25. 25.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 2 (d) 5
  26. 26.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 2 (d) 13
  27. 27.How many factors does 75 have? (a) 4 (b) 6 (c) 5 (d) 7
  28. 28.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 1 (d) 11
  29. 29.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
  30. 30.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 2 (d) 1
  31. 31.What is the prime factorisation of 252? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2 × 3² × 7 (d) 2³ × 3² × 7
  32. 32.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  33. 33.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 7 (d) 9
  34. 34.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
  35. 35.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 7 (d) 1
  36. 36.What is the smallest prime factor of 87? (a) 29 (b) 1 (c) 2 (d) 3
  37. 37.How many factors does 71 have? (a) 1 (b) 2 (c) 3 (d) 4
  38. 38.How many factors does 64 have? (a) 8 (b) 5 (c) 7 (d) 6
  39. 39.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
  40. 40.How many factors does 27 have? (a) 2 (b) 3 (c) 5 (d) 4

Answer key

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

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