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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 26 · 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 120? (a) 2 × 3 × 5³ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  2. 2.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 6 (d) 5
  3. 3.What is the smallest prime factor of 253? (a) 23 (b) 1 (c) 2 (d) 11
  4. 4.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 11 (d) 1
  5. 5.What is the prime factorisation of 14? (a) 2 × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2² × 7
  6. 6.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2² × 5 (d) 2 × 5³
  7. 7.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  8. 8.What is the smallest prime factor of 217? (a) 31 (b) 1 (c) 7 (d) 2
  9. 9.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13
  10. 10.How many factors does 95 have? (a) 5 (b) 4 (c) 2 (d) 3
  11. 11.How many factors does 92 have? (a) 5 (b) 7 (c) 6 (d) 4
  12. 12.How many factors does 74 have? (a) 4 (b) 3 (c) 2 (d) 5
  13. 13.How many factors does 23 have? (a) 3 (b) 4 (c) 2 (d) 1
  14. 14.How many prime numbers are there between 60 and 90? (a) 9 (b) 8 (c) 6 (d) 7
  15. 15.What is the smallest prime factor of 319? (a) 29 (b) 11 (c) 2 (d) 1
  16. 16.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2⁴ × 3² (d) 2² × 3²
  17. 17.What is the smallest prime factor of 65? (a) 5 (b) 1 (c) 2 (d) 13
  18. 18.How many factors does 63 have? (a) 6 (b) 5 (c) 4 (d) 7
  19. 19.What is the prime factorisation of 63? (a) 3² × 7 (b) 3 × 7 (c) 3³ × 7 (d) 3 × 7²
  20. 20.How many prime numbers are there between 30 and 60? (a) 7 (b) 6 (c) 8 (d) 9
  21. 21.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 5 (d) 1
  22. 22.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 3 (d) 2
  23. 23.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 1 (d) 2
  24. 24.How many factors does 41 have? (a) 4 (b) 3 (c) 1 (d) 2
  25. 25.How many factors does 100 have? (a) 7 (b) 10 (c) 8 (d) 9
  26. 26.How many factors does 115 have? (a) 3 (b) 4 (c) 2 (d) 5
  27. 27.How many factors does 65 have? (a) 4 (b) 5 (c) 2 (d) 3
  28. 28.What is the smallest prime factor of 93? (a) 31 (b) 1 (c) 3 (d) 2
  29. 29.What is the smallest prime factor of 247? (a) 13 (b) 2 (c) 19 (d) 1
  30. 30.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  31. 31.How many factors does 16 have? (a) 6 (b) 5 (c) 4 (d) 3
  32. 32.How many factors does 114 have? (a) 6 (b) 9 (c) 7 (d) 8
  33. 33.What is the smallest prime factor of 209? (a) 2 (b) 19 (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 smallest prime factor of 203? (a) 1 (b) 2 (c) 7 (d) 29
  36. 36.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2³ × 5 × 7
  37. 37.How many factors does 38 have? (a) 4 (b) 5 (c) 3 (d) 2
  38. 38.How many factors does 106 have? (a) 3 (b) 4 (c) 2 (d) 5
  39. 39.How many factors does 111 have? (a) 4 (b) 2 (c) 3 (d) 5
  40. 40.What is the smallest prime factor of 377? (a) 13 (b) 29 (c) 2 (d) 1

Answer key

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

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