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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 186 · 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 420? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  2. 2.How many factors does 33 have? (a) 4 (b) 5 (c) 2 (d) 3
  3. 3.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7 (d) 2 × 5 × 7²
  4. 4.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 4 (d) 1
  5. 5.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5³ (d) 2⁴ × 3 × 5
  6. 6.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 1 (d) 11
  7. 7.What is the smallest prime factor of 95? (a) 19 (b) 1 (c) 5 (d) 2
  8. 8.How many factors does 12 have? (a) 4 (b) 6 (c) 7 (d) 5
  9. 9.How many factors does 101 have? (a) 1 (b) 4 (c) 2 (d) 3
  10. 10.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  11. 11.How many factors does 19 have? (a) 1 (b) 4 (c) 2 (d) 3
  12. 12.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2 × 3 × 7² (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  13. 13.How many prime numbers are there between 30 and 40? (a) 4 (b) 2 (c) 1 (d) 3
  14. 14.What is the smallest prime factor of 319? (a) 11 (b) 29 (c) 1 (d) 2
  15. 15.How many factors does 95 have? (a) 4 (b) 2 (c) 5 (d) 3
  16. 16.How many factors does 66 have? (a) 8 (b) 6 (c) 9 (d) 7
  17. 17.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 7 (d) 6
  18. 18.What is the smallest prime factor of 77? (a) 2 (b) 1 (c) 7 (d) 11
  19. 19.How many factors does 99 have? (a) 4 (b) 5 (c) 7 (d) 6
  20. 20.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 2 (d) 1
  21. 21.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2⁵ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
  22. 22.What is the prime factorisation of 36? (a) 2 × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2³ × 3²
  23. 23.How many factors does 119 have? (a) 2 (b) 5 (c) 3 (d) 4
  24. 24.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 1 (d) 4
  25. 25.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
  26. 26.How many factors does 68 have? (a) 6 (b) 7 (c) 5 (d) 4
  27. 27.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2³ × 5
  28. 28.How many prime numbers are there between 80 and 110? (a) 6 (b) 9 (c) 7 (d) 8
  29. 29.How many factors does 57 have? (a) 5 (b) 2 (c) 3 (d) 4
  30. 30.How many factors does 117 have? (a) 7 (b) 6 (c) 4 (d) 5
  31. 31.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 1 (d) 3
  32. 32.What is the smallest prime factor of 55? (a) 11 (b) 2 (c) 1 (d) 5
  33. 33.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  34. 34.How many factors does 15 have? (a) 5 (b) 4 (c) 3 (d) 2
  35. 35.How many factors does 47 have? (a) 3 (b) 4 (c) 2 (d) 1
  36. 36.How many prime numbers are there between 30 and 50? (a) 7 (b) 5 (c) 6 (d) 4
  37. 37.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 4 (d) 3
  38. 38.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2⁴ × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
  39. 39.How many factors does 62 have? (a) 2 (b) 3 (c) 5 (d) 4
  40. 40.How many prime numbers are there between 20 and 50? (a) 6 (b) 9 (c) 8 (d) 7

Answer key

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

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