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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 48 · 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 prime numbers are there between 40 and 60? (a) 5 (b) 4 (c) 6 (d) 7
  2. 2.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3³ × 5 × 7
  3. 3.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
  4. 4.How many prime numbers are there between 20 and 40? (a) 4 (b) 3 (c) 6 (d) 5
  5. 5.What is the smallest prime factor of 187? (a) 11 (b) 1 (c) 17 (d) 2
  6. 6.How many prime numbers are there between 20 and 50? (a) 7 (b) 9 (c) 6 (d) 8
  7. 7.How many factors does 24 have? (a) 7 (b) 6 (c) 8 (d) 9
  8. 8.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2
  9. 9.How many factors does 75 have? (a) 4 (b) 6 (c) 5 (d) 7
  10. 10.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 1 (d) 2
  11. 11.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 1 (d) 4
  12. 12.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 2 (d) 1
  13. 13.How many prime numbers are there between 40 and 70? (a) 6 (b) 7 (c) 8 (d) 9
  14. 14.What is the smallest prime factor of 51? (a) 2 (b) 1 (c) 17 (d) 3
  15. 15.How many factors does 23 have? (a) 3 (b) 2 (c) 4 (d) 1
  16. 16.How many factors does 44 have? (a) 5 (b) 6 (c) 4 (d) 7
  17. 17.What is the smallest prime factor of 299? (a) 2 (b) 13 (c) 1 (d) 23
  18. 18.How many prime numbers are there between 10 and 40? (a) 7 (b) 9 (c) 8 (d) 10
  19. 19.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5
  20. 20.How many prime numbers are there between 10 and 30? (a) 5 (b) 7 (c) 8 (d) 6
  21. 21.What is the smallest prime factor of 169? (a) 2 (b) 1 (c) 3 (d) 13
  22. 22.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 2 (d) 11
  23. 23.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 5 (d) 4
  24. 24.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  25. 25.How many factors does 69 have? (a) 4 (b) 3 (c) 2 (d) 5
  26. 26.How many factors does 101 have? (a) 4 (b) 3 (c) 2 (d) 1
  27. 27.How many prime numbers are there between 50 and 60? (a) 3 (b) 2 (c) 1 (d) 4
  28. 28.How many prime numbers are there between 80 and 110? (a) 7 (b) 8 (c) 9 (d) 6
  29. 29.How many factors does 94 have? (a) 3 (b) 5 (c) 4 (d) 2
  30. 30.How many factors does 98 have? (a) 4 (b) 5 (c) 6 (d) 7
  31. 31.How many factors does 39 have? (a) 4 (b) 2 (c) 3 (d) 5
  32. 32.How many factors does 95 have? (a) 4 (b) 5 (c) 3 (d) 2
  33. 33.How many factors does 42 have? (a) 7 (b) 9 (c) 6 (d) 8
  34. 34.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 3 (d) 4
  35. 35.How many factors does 63 have? (a) 4 (b) 5 (c) 6 (d) 7
  36. 36.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2⁵ × 3 (d) 2 × 3⁴
  37. 37.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
  38. 38.How many factors does 31 have? (a) 1 (b) 3 (c) 2 (d) 4
  39. 39.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
  40. 40.How many factors does 59 have? (a) 4 (b) 2 (c) 3 (d) 1

Answer key

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

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