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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 13 · 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 prime factorisation of 14? (a) 2 × 7² (b) 2³ × 7 (c) 2 × 7 (d) 2² × 7
  2. 2.How many factors does 35 have? (a) 2 (b) 4 (c) 5 (d) 3
  3. 3.How many factors does 55 have? (a) 2 (b) 3 (c) 4 (d) 5
  4. 4.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
  5. 5.What is the smallest prime factor of 33? (a) 2 (b) 3 (c) 1 (d) 11
  6. 6.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2³ × 3² (c) 2⁵ × 3² (d) 2⁴ × 3²
  7. 7.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  8. 8.How many factors does 22 have? (a) 4 (b) 5 (c) 2 (d) 3
  9. 9.How many prime numbers are there between 70 and 80? (a) 5 (b) 4 (c) 3 (d) 2
  10. 10.How many prime numbers are there between 60 and 90? (a) 9 (b) 6 (c) 7 (d) 8
  11. 11.What is the smallest prime factor of 119? (a) 7 (b) 2 (c) 1 (d) 17
  12. 12.How many prime numbers are there between 90 and 110? (a) 7 (b) 5 (c) 4 (d) 6
  13. 13.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2⁴ × 3² (c) 2² × 3³ (d) 2² × 3²
  14. 14.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 5 (d) 3
  15. 15.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
  16. 16.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 7 (d) 9
  17. 17.What is the prime factorisation of 28? (a) 2² × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2 × 7
  18. 18.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
  19. 19.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 2 (d) 1
  20. 20.What is the smallest prime factor of 115? (a) 2 (b) 23 (c) 1 (d) 5
  21. 21.What is the smallest prime factor of 187? (a) 11 (b) 1 (c) 2 (d) 17
  22. 22.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
  23. 23.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7 (c) 3² × 7 (d) 3 × 7²
  24. 24.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  25. 25.How many factors does 28 have? (a) 4 (b) 7 (c) 6 (d) 5
  26. 26.How many factors does 97 have? (a) 2 (b) 4 (c) 3 (d) 1
  27. 27.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5³
  28. 28.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2² × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
  29. 29.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 3 (d) 4
  30. 30.How many factors does 84 have? (a) 11 (b) 10 (c) 13 (d) 12
  31. 31.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 7 (d) 13
  32. 32.What is the smallest prime factor of 341? (a) 1 (b) 11 (c) 31 (d) 2
  33. 33.What is the smallest prime factor of 93? (a) 1 (b) 31 (c) 2 (d) 3
  34. 34.What is the prime factorisation of 12? (a) 2 × 3 (b) 2² × 3 (c) 2 × 3² (d) 2³ × 3
  35. 35.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 3 (d) 29
  36. 36.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
  37. 37.What is the smallest prime factor of 377? (a) 1 (b) 29 (c) 2 (d) 13
  38. 38.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  39. 39.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2³ × 5 (d) 2² × 5
  40. 40.How many factors does 38 have? (a) 5 (b) 2 (c) 3 (d) 4

Answer key

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

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