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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 94 · 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 95? (a) 5 (b) 19 (c) 2 (d) 1
  2. 2.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7² (d) 2 × 3² × 7
  3. 3.What is the prime factorisation of 35? (a) 5 × 7 (b) 5 × 7² (c) 5² × 7 (d) 5³ × 7
  4. 4.What is the smallest prime factor of 51? (a) 2 (b) 1 (c) 17 (d) 3
  5. 5.How many factors does 76 have? (a) 4 (b) 6 (c) 7 (d) 5
  6. 6.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
  7. 7.What is the smallest prime factor of 85? (a) 17 (b) 1 (c) 5 (d) 2
  8. 8.How many prime numbers are there between 10 and 20? (a) 3 (b) 5 (c) 4 (d) 6
  9. 9.How many factors does 82 have? (a) 4 (b) 2 (c) 3 (d) 5
  10. 10.What is the smallest prime factor of 91? (a) 1 (b) 13 (c) 2 (d) 7
  11. 11.How many factors does 28 have? (a) 5 (b) 7 (c) 4 (d) 6
  12. 12.What is the smallest prime factor of 161? (a) 2 (b) 23 (c) 7 (d) 1
  13. 13.What is the smallest prime factor of 69? (a) 1 (b) 2 (c) 3 (d) 23
  14. 14.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5 (c) 2 × 5² (d) 2³ × 5
  15. 15.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁵ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁴ × 3 × 5
  16. 16.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5²
  17. 17.What is the prime factorisation of 180? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
  18. 18.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 1 (d) 11
  19. 19.How many factors does 95 have? (a) 2 (b) 5 (c) 4 (d) 3
  20. 20.What is the smallest prime factor of 121? (a) 3 (b) 11 (c) 1 (d) 2
  21. 21.How many factors does 13 have? (a) 4 (b) 2 (c) 1 (d) 3
  22. 22.How many factors does 105 have? (a) 7 (b) 6 (c) 9 (d) 8
  23. 23.How many prime numbers are there between 40 and 70? (a) 9 (b) 7 (c) 6 (d) 8
  24. 24.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 2 (d) 4
  25. 25.How many prime numbers are there between 30 and 60? (a) 7 (b) 6 (c) 9 (d) 8
  26. 26.How many prime numbers are there between 30 and 50? (a) 6 (b) 5 (c) 7 (d) 4
  27. 27.How many factors does 39 have? (a) 3 (b) 2 (c) 4 (d) 5
  28. 28.How many factors does 89 have? (a) 2 (b) 1 (c) 4 (d) 3
  29. 29.How many factors does 46 have? (a) 5 (b) 3 (c) 4 (d) 2
  30. 30.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
  31. 31.How many factors does 115 have? (a) 4 (b) 2 (c) 5 (d) 3
  32. 32.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  33. 33.What is the smallest prime factor of 221? (a) 17 (b) 13 (c) 2 (d) 1
  34. 34.How many prime numbers are there between 50 and 70? (a) 6 (b) 5 (c) 4 (d) 3
  35. 35.How many factors does 110 have? (a) 6 (b) 9 (c) 7 (d) 8
  36. 36.How many factors does 48 have? (a) 9 (b) 11 (c) 10 (d) 8
  37. 37.What is the smallest prime factor of 203? (a) 29 (b) 7 (c) 2 (d) 1
  38. 38.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7²
  39. 39.What is the smallest prime factor of 169? (a) 3 (b) 2 (c) 1 (d) 13
  40. 40.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 3 (d) 5

Answer key

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

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