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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 183 · 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 45 have? (a) 4 (b) 6 (c) 5 (d) 7
  2. 2.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 6 (d) 5
  3. 3.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  4. 4.How many factors does 77 have? (a) 3 (b) 5 (c) 2 (d) 4
  5. 5.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
  6. 6.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 6 (d) 7
  7. 7.How many factors does 73 have? (a) 1 (b) 4 (c) 3 (d) 2
  8. 8.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  9. 9.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 5 (d) 4
  10. 10.How many prime numbers are there between 10 and 40? (a) 9 (b) 10 (c) 7 (d) 8
  11. 11.What is the smallest prime factor of 115? (a) 1 (b) 2 (c) 23 (d) 5
  12. 12.What is the prime factorisation of 210? (a) 2³ × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
  13. 13.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  14. 14.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
  15. 15.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2² × 5 (d) 2³ × 5
  16. 16.How many factors does 40 have? (a) 7 (b) 6 (c) 8 (d) 9
  17. 17.What is the prime factorisation of 56? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7³ (d) 2⁴ × 7
  18. 18.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2³ × 5 (c) 2² × 5 (d) 2⁴ × 5
  19. 19.How many factors does 95 have? (a) 5 (b) 4 (c) 2 (d) 3
  20. 20.How many factors does 111 have? (a) 5 (b) 3 (c) 2 (d) 4
  21. 21.What is the prime factorisation of 180? (a) 2 × 3² × 5 (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
  22. 22.How many factors does 52 have? (a) 5 (b) 4 (c) 7 (d) 6
  23. 23.What is the smallest prime factor of 55? (a) 2 (b) 1 (c) 5 (d) 11
  24. 24.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 5 (d) 13
  25. 25.How many prime numbers are there between 80 and 90? (a) 3 (b) 4 (c) 1 (d) 2
  26. 26.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2 × 3³ (c) 2² × 3 (d) 2³ × 3
  27. 27.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7³
  28. 28.What is the smallest prime factor of 155? (a) 1 (b) 31 (c) 2 (d) 5
  29. 29.How many factors does 24 have? (a) 6 (b) 9 (c) 8 (d) 7
  30. 30.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 9 (d) 8
  31. 31.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 7 (d) 31
  32. 32.How many factors does 107 have? (a) 4 (b) 3 (c) 1 (d) 2
  33. 33.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  34. 34.How many factors does 27 have? (a) 2 (b) 5 (c) 3 (d) 4
  35. 35.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 5 (d) 4
  36. 36.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 2 (d) 1
  37. 37.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5³ (d) 2⁴ × 3 × 5
  38. 38.How many factors does 99 have? (a) 4 (b) 7 (c) 5 (d) 6
  39. 39.How many factors does 16 have? (a) 5 (b) 3 (c) 4 (d) 6
  40. 40.What is the smallest prime factor of 209? (a) 11 (b) 19 (c) 1 (d) 2

Answer key

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

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