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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 111 · 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 70 and 90? (a) 7 (b) 6 (c) 5 (d) 4
  2. 2.What is the prime factorisation of 56? (a) 2² × 7 (b) 2 × 7³ (c) 2³ × 7 (d) 2⁴ × 7
  3. 3.What is the prime factorisation of 18? (a) 2² × 3 (b) 2² × 3² (c) 2 × 3³ (d) 2 × 3²
  4. 4.How many factors does 107 have? (a) 3 (b) 1 (c) 2 (d) 4
  5. 5.How many factors does 59 have? (a) 2 (b) 4 (c) 3 (d) 1
  6. 6.What is the prime factorisation of 28? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2 × 7
  7. 7.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁴ × 3 (d) 2⁵ × 3
  8. 8.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  9. 9.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  10. 10.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 13 (d) 7
  11. 11.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 5 (d) 8
  12. 12.How many factors does 50 have? (a) 6 (b) 5 (c) 4 (d) 7
  13. 13.How many factors does 66 have? (a) 7 (b) 6 (c) 9 (d) 8
  14. 14.How many prime numbers are there between 60 and 80? (a) 7 (b) 4 (c) 5 (d) 6
  15. 15.How many factors does 67 have? (a) 4 (b) 2 (c) 3 (d) 1
  16. 16.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 3 (d) 4
  17. 17.How many factors does 106 have? (a) 5 (b) 3 (c) 2 (d) 4
  18. 18.How many factors does 88 have? (a) 6 (b) 8 (c) 7 (d) 9
  19. 19.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  20. 20.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 6 (d) 5
  21. 21.How many factors does 12 have? (a) 4 (b) 6 (c) 5 (d) 7
  22. 22.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 3 (d) 4
  23. 23.What is the smallest prime factor of 145? (a) 2 (b) 29 (c) 1 (d) 5
  24. 24.How many factors does 86 have? (a) 2 (b) 3 (c) 4 (d) 5
  25. 25.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 1 (d) 5
  26. 26.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2³ × 3² × 5
  27. 27.How many factors does 112 have? (a) 9 (b) 11 (c) 8 (d) 10
  28. 28.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 11 (d) 2
  29. 29.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 2 (d) 29
  30. 30.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2² × 5 × 7
  31. 31.What is the smallest prime factor of 57? (a) 3 (b) 1 (c) 2 (d) 19
  32. 32.How many factors does 73 have? (a) 4 (b) 3 (c) 1 (d) 2
  33. 33.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁴ × 3² (d) 2⁵ × 3²
  34. 34.How many prime numbers are there between 50 and 80? (a) 8 (b) 7 (c) 6 (d) 9
  35. 35.How many factors does 70 have? (a) 6 (b) 9 (c) 8 (d) 7
  36. 36.How many prime numbers are there between 40 and 70? (a) 6 (b) 9 (c) 7 (d) 8
  37. 37.What is the smallest prime factor of 319? (a) 2 (b) 1 (c) 11 (d) 29
  38. 38.What is the smallest prime factor of 35? (a) 5 (b) 1 (c) 2 (d) 7
  39. 39.What is the smallest prime factor of 93? (a) 2 (b) 3 (c) 31 (d) 1
  40. 40.How many factors does 72 have? (a) 13 (b) 12 (c) 11 (d) 10

Answer key

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

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