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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 207 · 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 91 have? (a) 5 (b) 2 (c) 4 (d) 3
  2. 2.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7² (d) 2 × 7
  3. 3.How many factors does 14 have? (a) 3 (b) 5 (c) 4 (d) 2
  4. 4.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2 × 3³ (c) 2⁴ × 3 (d) 2² × 3
  5. 5.How many factors does 110 have? (a) 6 (b) 7 (c) 8 (d) 9
  6. 6.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 5 (d) 6
  7. 7.How many factors does 45 have? (a) 6 (b) 4 (c) 5 (d) 7
  8. 8.What is the smallest prime factor of 341? (a) 2 (b) 1 (c) 11 (d) 31
  9. 9.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
  10. 10.What is the smallest prime factor of 319? (a) 2 (b) 11 (c) 1 (d) 29
  11. 11.How many prime numbers are there between 70 and 90? (a) 4 (b) 5 (c) 6 (d) 7
  12. 12.How many factors does 88 have? (a) 7 (b) 6 (c) 9 (d) 8
  13. 13.How many factors does 22 have? (a) 2 (b) 3 (c) 5 (d) 4
  14. 14.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 2 (d) 4
  15. 15.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 11 (d) 3
  16. 16.How many factors does 16 have? (a) 5 (b) 6 (c) 4 (d) 3
  17. 17.How many factors does 113 have? (a) 2 (b) 3 (c) 1 (d) 4
  18. 18.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2² × 5 × 7
  19. 19.How many factors does 61 have? (a) 2 (b) 1 (c) 4 (d) 3
  20. 20.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 6 (d) 4
  21. 21.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
  22. 22.How many prime numbers are there between 30 and 50? (a) 4 (b) 6 (c) 5 (d) 7
  23. 23.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁴ × 5 (c) 2⁵ × 5 (d) 2³ × 5
  24. 24.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 2 (d) 3
  25. 25.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 7 (d) 6
  26. 26.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
  27. 27.How many factors does 53 have? (a) 1 (b) 3 (c) 4 (d) 2
  28. 28.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 2 (d) 7
  29. 29.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 29 (d) 3
  30. 30.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 2 (d) 1
  31. 31.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  32. 32.How many factors does 104 have? (a) 8 (b) 9 (c) 6 (d) 7
  33. 33.What is the smallest prime factor of 253? (a) 23 (b) 2 (c) 11 (d) 1
  34. 34.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 5 (d) 7
  35. 35.What is the prime factorisation of 315? (a) 3³ × 5 × 7 (b) 3² × 5 × 7 (c) 3 × 5 × 7² (d) 3 × 5 × 7
  36. 36.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 5 (d) 7
  37. 37.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
  38. 38.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
  39. 39.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  40. 40.What is the smallest prime factor of 55? (a) 11 (b) 5 (c) 2 (d) 1

Answer key

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

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