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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 139 · 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 247? (a) 19 (b) 2 (c) 13 (d) 1
  2. 2.How many factors does 47 have? (a) 3 (b) 4 (c) 2 (d) 1
  3. 3.How many prime numbers are there between 90 and 110? (a) 7 (b) 5 (c) 4 (d) 6
  4. 4.How many prime numbers are there between 60 and 80? (a) 6 (b) 5 (c) 4 (d) 7
  5. 5.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  6. 6.How many factors does 21 have? (a) 3 (b) 5 (c) 2 (d) 4
  7. 7.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 6 (d) 7
  8. 8.What is the smallest prime factor of 49? (a) 7 (b) 2 (c) 3 (d) 1
  9. 9.How many factors does 53 have? (a) 4 (b) 2 (c) 3 (d) 1
  10. 10.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2² × 3 (c) 2⁴ × 3 (d) 2 × 3³
  11. 11.What is the smallest prime factor of 77? (a) 1 (b) 7 (c) 11 (d) 2
  12. 12.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  13. 13.How many prime numbers are there between 30 and 40? (a) 2 (b) 3 (c) 4 (d) 1
  14. 14.How many factors does 56 have? (a) 6 (b) 7 (c) 9 (d) 8
  15. 15.What is the smallest prime factor of 91? (a) 7 (b) 2 (c) 1 (d) 13
  16. 16.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 2 (d) 11
  17. 17.How many factors does 26 have? (a) 2 (b) 3 (c) 5 (d) 4
  18. 18.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3³ × 5 × 7
  19. 19.How many factors does 28 have? (a) 7 (b) 6 (c) 5 (d) 4
  20. 20.How many factors does 115 have? (a) 3 (b) 2 (c) 4 (d) 5
  21. 21.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 1 (d) 3
  22. 22.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
  23. 23.How many factors does 35 have? (a) 3 (b) 5 (c) 2 (d) 4
  24. 24.How many factors does 94 have? (a) 2 (b) 5 (c) 3 (d) 4
  25. 25.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
  26. 26.What is the smallest prime factor of 95? (a) 2 (b) 1 (c) 19 (d) 5
  27. 27.How many prime numbers are there between 10 and 40? (a) 8 (b) 10 (c) 9 (d) 7
  28. 28.What is the smallest prime factor of 169? (a) 1 (b) 2 (c) 13 (d) 3
  29. 29.How many prime numbers are there between 70 and 90? (a) 5 (b) 7 (c) 6 (d) 4
  30. 30.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
  31. 31.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 6 (d) 5
  32. 32.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7³ (d) 2⁴ × 7
  33. 33.How many factors does 25 have? (a) 2 (b) 4 (c) 3 (d) 1
  34. 34.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 11 (d) 1
  35. 35.How many factors does 103 have? (a) 2 (b) 4 (c) 3 (d) 1
  36. 36.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7³
  37. 37.How many factors does 72 have? (a) 13 (b) 11 (c) 12 (d) 10
  38. 38.What is the smallest prime factor of 221? (a) 17 (b) 1 (c) 2 (d) 13
  39. 39.How many factors does 14 have? (a) 3 (b) 4 (c) 5 (d) 2
  40. 40.What is the smallest prime factor of 119? (a) 17 (b) 1 (c) 2 (d) 7

Answer key

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

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