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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 2 · 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 55? (a) 1 (b) 2 (c) 11 (d) 5
  2. 2.How many factors does 108 have? (a) 10 (b) 11 (c) 13 (d) 12
  3. 3.What is the smallest prime factor of 299? (a) 23 (b) 2 (c) 13 (d) 1
  4. 4.How many factors does 94 have? (a) 2 (b) 3 (c) 5 (d) 4
  5. 5.How many factors does 98 have? (a) 7 (b) 6 (c) 5 (d) 4
  6. 6.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  7. 7.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 11 (d) 1
  8. 8.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2³ × 5
  9. 9.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 8 (d) 10
  10. 10.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 5 (d) 4
  11. 11.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5³ (d) 2² × 3 × 5
  12. 12.How many factors does 100 have? (a) 9 (b) 7 (c) 8 (d) 10
  13. 13.What is the prime factorisation of 14? (a) 2 × 7 (b) 2³ × 7 (c) 2² × 7 (d) 2 × 7²
  14. 14.How many factors does 24 have? (a) 6 (b) 8 (c) 7 (d) 9
  15. 15.What is the smallest prime factor of 35? (a) 2 (b) 7 (c) 1 (d) 5
  16. 16.How many factors does 110 have? (a) 9 (b) 8 (c) 6 (d) 7
  17. 17.How many prime numbers are there between 80 and 100? (a) 3 (b) 5 (c) 2 (d) 4
  18. 18.How many factors does 95 have? (a) 5 (b) 3 (c) 2 (d) 4
  19. 19.How many factors does 23 have? (a) 4 (b) 3 (c) 1 (d) 2
  20. 20.How many factors does 106 have? (a) 3 (b) 5 (c) 2 (d) 4
  21. 21.How many factors does 19 have? (a) 4 (b) 3 (c) 1 (d) 2
  22. 22.What is the prime factorisation of 336? (a) 2 × 3 × 7⁴ (b) 2⁴ × 3 × 7 (c) 2⁵ × 3 × 7 (d) 2³ × 3 × 7
  23. 23.How many prime numbers are there between 90 and 120? (a) 6 (b) 8 (c) 5 (d) 7
  24. 24.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁵ × 3 (d) 2⁴ × 3
  25. 25.What is the smallest prime factor of 49? (a) 1 (b) 3 (c) 2 (d) 7
  26. 26.What is the prime factorisation of 45? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
  27. 27.How many factors does 73 have? (a) 3 (b) 1 (c) 2 (d) 4
  28. 28.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 7 (d) 5
  29. 29.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7³ (d) 2³ × 3² × 7
  30. 30.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 7 (d) 9
  31. 31.How many factors does 29 have? (a) 3 (b) 2 (c) 4 (d) 1
  32. 32.How many factors does 38 have? (a) 2 (b) 5 (c) 3 (d) 4
  33. 33.What is the smallest prime factor of 187? (a) 2 (b) 1 (c) 11 (d) 17
  34. 34.How many prime numbers are there between 40 and 70? (a) 8 (b) 7 (c) 6 (d) 9
  35. 35.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 2 (d) 11
  36. 36.How many prime numbers are there between 70 and 80? (a) 3 (b) 2 (c) 4 (d) 5
  37. 37.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2² × 3² (d) 2 × 3²
  38. 38.How many factors does 82 have? (a) 2 (b) 5 (c) 4 (d) 3
  39. 39.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3⁴ (d) 2⁵ × 3²
  40. 40.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4

Answer key

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

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