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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 77 · 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 99 have? (a) 5 (b) 6 (c) 4 (d) 7
  2. 2.What is the prime factorisation of 72? (a) 2² × 3² (b) 2⁴ × 3² (c) 2² × 3³ (d) 2³ × 3²
  3. 3.What is the prime factorisation of 15? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
  4. 4.How many factors does 57 have? (a) 2 (b) 3 (c) 5 (d) 4
  5. 5.How many factors does 12 have? (a) 6 (b) 5 (c) 4 (d) 7
  6. 6.How many factors does 15 have? (a) 5 (b) 3 (c) 4 (d) 2
  7. 7.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 11 (d) 2
  8. 8.How many factors does 119 have? (a) 5 (b) 3 (c) 4 (d) 2
  9. 9.How many factors does 81 have? (a) 3 (b) 5 (c) 6 (d) 4
  10. 10.How many prime numbers are there between 70 and 90? (a) 4 (b) 6 (c) 7 (d) 5
  11. 11.How many factors does 60 have? (a) 13 (b) 11 (c) 10 (d) 12
  12. 12.How many prime numbers are there between 50 and 70? (a) 4 (b) 6 (c) 5 (d) 3
  13. 13.How many factors does 89 have? (a) 1 (b) 4 (c) 2 (d) 3
  14. 14.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
  15. 15.How many factors does 32 have? (a) 4 (b) 5 (c) 6 (d) 7
  16. 16.How many factors does 87 have? (a) 3 (b) 5 (c) 2 (d) 4
  17. 17.What is the smallest prime factor of 161? (a) 7 (b) 23 (c) 1 (d) 2
  18. 18.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 1 (d) 7
  19. 19.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 6 (d) 9
  20. 20.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  21. 21.How many prime numbers are there between 60 and 70? (a) 3 (b) 1 (c) 4 (d) 2
  22. 22.How many factors does 18 have? (a) 7 (b) 5 (c) 4 (d) 6
  23. 23.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁴ × 3² (c) 2⁵ × 3² (d) 2² × 3⁴
  24. 24.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5 (c) 2² × 5 (d) 2 × 5²
  25. 25.How many factors does 65 have? (a) 2 (b) 4 (c) 3 (d) 5
  26. 26.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7³
  27. 27.How many factors does 53 have? (a) 2 (b) 4 (c) 1 (d) 3
  28. 28.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 5 (d) 4
  29. 29.What is the smallest prime factor of 93? (a) 31 (b) 1 (c) 3 (d) 2
  30. 30.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7² (d) 2 × 7
  31. 31.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2² × 3 × 5
  32. 32.How many factors does 21 have? (a) 2 (b) 3 (c) 4 (d) 5
  33. 33.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 2 (d) 3
  34. 34.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2 × 3⁴ (c) 2³ × 3 (d) 2⁵ × 3
  35. 35.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 0 (d) 2
  36. 36.What is the smallest prime factor of 69? (a) 23 (b) 2 (c) 1 (d) 3
  37. 37.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
  38. 38.What is the smallest prime factor of 247? (a) 2 (b) 1 (c) 13 (d) 19
  39. 39.How many factors does 13 have? (a) 3 (b) 4 (c) 1 (d) 2
  40. 40.How many prime numbers are there between 30 and 40? (a) 1 (b) 4 (c) 3 (d) 2

Answer key

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

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